Filed pursuant to Rule 424(b)(3)
File No. 333-249435

PIMCO Income Strategy Fund

Supplement dated May 3, 2021 to the Fund’s Prospectus and Statement of Additional Information dated November 25, 2020, each as supplemented from time to time (respectively, the “Prospectus” and the “SAI”)

Effective immediately, the fifth paragraph of the “Prospectus Summary—Leverage” section of the Prospectus is deleted and replaced with the following:

Regarding the costs associated with the Fund’s ARPS, the terms of the ARPS provide that they would ordinarily pay dividends at a rate set at auctions held every seven days, normally payable on the first business day following the end of the rate period, subject to a maximum applicable rate calculated as a function of the ARPS’ then-current rating and a reference interest rate. However, the weekly auctions for the ARPS, as well as auctions for similar preferred shares of other closed-end funds in the U.S., have failed since February 2008, and the dividend rates on the ARPS since that time have been paid at the maximum applicable rate (i.e., the greater of a multiple of or a spread plus a reference rate, which is the greater of the applicable LIBOR rate or the applicable Treasury Index Rate). In September 2011, Moody’s, a ratings agency that provides ratings for the Fund’s ARPS, downgraded its rating of the ARPS from “Aaa” to “Aa2,” citing what it believed to be persistently thin asset coverage levels, increased NAV volatility and concerns about secondary market liquidity for some assets supporting rated obligations. In July 2012, Moody’s downgraded its rating of the ARPS from “Aa2” to “Aa3” pursuant to a revised ratings methodology adopted by Moody’s. In May 2020, Fitch downgraded its rating of the ARPS from “AAA” to “AA,” indicating the downgrades reflected recent extreme market volatility and reduced asset liquidity, which it believed had quickly eroded asset coverage cushions for closed-end funds and challenged fund managers’ ability to deleverage. On December 4, 2020, Fitch published ratings criteria relating to closed-end fund obligations, including preferred shares, which effectively result in a rating cap of “AA” for debt and preferred stock issued by closed-end funds and a rating cap of “A” for (i) debt and preferred shares issued by closed-end funds exposed to corporate debt, emerging market debt, below-investment-grade and unrated debt, structured securities and equity, (ii) and closed-end funds with material exposure to “BBB” category rated assets. Following the close of business on April 30, 2021, Fitch downgraded its rating of the ARPS from “AA” to “A” pursuant to the revised ratings methodology and related new rating caps. The Fund expects that the ARPS will continue to pay dividends at the maximum applicable rate for the foreseeable future and cannot predict whether or when the auction markets for the ARPS may resume normal functioning. See “Use of Leverage,” “Principal Risks of the Fund—Leverage Risk,” “Principal Risks of the Fund—Additional Risks Associated with the Fund’s Preferred Shares” and “Description of Capital Structure” for more information.

In addition, effective immediately, following paragraph is added after first paragraph of the “Principal Risks of the Fund—Additional Risks Associated with the Fund’s Preferred Shares” section of the Prospectus Summary and the first paragraph of the “Principal Risks of the Fund—Additional Risks Associated with the Fund’s Preferred Shares” section of the Prospectus:

In addition, the multiple used to calculate the maximum applicable rate is based in part on the credit rating assigned to the ARPS by the applicable rating agency (currently, Moody’s and Fitch), with the multiple generally increasing as the rating declines below certain levels. In September 2011, Moody’s, a ratings agency that provides ratings for the Fund’s ARPS, downgraded its rating of the ARPS from “Aaa” to “Aa2,” citing what it believed to be persistently thin asset coverage levels, increased NAV volatility and concerns about secondary market liquidity for some assets supporting rated obligations. Under the Bylaws, the 2011 Moody’s downgrade resulted in an increase in the dividend rate multiplier from 1.25 to 1.50, thereby increasing the dividend rate payable to ARPS holders and increasing the costs to Common Shareholders associated with the Fund’s leverage. See “Use of Leverage” and “Description of Capital Structure.” In July 2012, Moody’s downgraded its rating of the ARPS from “Aa2” to “Aa3” pursuant to a revised ratings methodology adopted by Moody’s. In May 2020, Fitch downgraded its rating of the ARPS from “AAA” to “AA,” indicating the downgrades reflected recent extreme market volatility and reduced asset liquidity, which it believed had quickly eroded asset coverage cushions for closed-end funds and challenged fund managers’ ability to deleverage. Under the Bylaws, the 2020 Fitch downgrade resulted in an increase in the applicable spread over the reference rate from 125 bps to 150 bps,

thereby increasing the dividend rate payable to ARPS holders and increasing the costs to Common Shareholders associated with the Fund’s leverage. On December 4, 2020, Fitch published ratings criteria relating to closed-end fund obligations, including preferred shares, which effectively result in a rating cap of “AA” for debt and preferred stock issued by closed-end funds and a rating cap of “A” for (i) debt and preferred shares issued by closed-end funds exposed to corporate debt, emerging market debt, below-investment-grade and unrated debt, structured securities and equity, (ii) and closed-end funds with material exposure to “BBB” category rated assets. Following the close of business on April 30, 2021, Fitch downgraded its rating of the ARPS from “AA” to “A” pursuant to the revised ratings methodology and related new rating caps. Under the Bylaws, the April 2021 Fitch downgrade resulted in an increase in the dividend rate multiplier from 1.50 to 2.00, which could increase the dividend rate payable to ARPS holders should the maximum dividend rate be determined via the multiplier in lieu of the spread noted above (the maximum dividend rate is based on the greater of a multiple of or a spread plus a reference rate) and, thereby, increase the expenses to Common Shareholders associated with the Fund’s leverage. See “Use of Leverage” and “Description of Capital Structure.” It is possible for the ARPS to be further downgraded in the future, possibly resulting in further increases to the maximum applicable rate and, thereby, the expenses borne by the Fund’s Common Shareholders.

In addition, effective immediately, the fourth paragraph of the “Principal Risks of the Fund—Additional Risks Associated with the Fund’s Preferred Shares” section of the Prospectus Summary and the fourth paragraph of the “Principal Risks of the Fund – Additional Risks Associated with the Fund’s Preferred Shares” section of the Prospectus are deleted and replaced with the following:

The ratings agencies that have assigned ratings to the Fund’s preferred shares may change their rating methodologies for evaluating and providing ratings for shares of closed-end funds at any time and in their sole discretion, perhaps substantially. Such a change could adversely affect the ratings assigned to the Fund’s Preferred Shares, the dividend rates paid thereon, and the expenses borne by the Fund’s Common Shareholders. For instance, on December 4, 2020, Fitch published ratings criteria relating to closed-end fund obligations, including preferred shares, which effectively result in a rating cap of “AA” for debt and preferred stock issued by closed-end funds and a rating cap of “A” for (i) debt and preferred shares issued by closed-end funds exposed to corporate debt, emerging market debt, below-investment-grade and unrated debt, structured securities and equity, (ii) and closed-end funds with material exposure to “BBB” category rated assets. The updated Fitch ratings criteria effectively capped the credit rating of the Fund’s ARPS at “A”. Following the close of business on April 30, 2021, Fitch downgraded its rating of the ARPS from “AA” to “A” pursuant to the updated Fitch ratings criteria and related new rating caps. Under the Bylaws, the April 2021 Fitch downgrade resulted in an increase in the dividend rate multiplier from 1.50 to 2.00, which could increase the dividend rate payable to ARPS holders should the maximum dividend rate be determined via the multiplier in lieu of the spread noted above (the maximum dividend rate is based on the greater of a multiple of or a spread plus a reference rate) and, thereby, increase the expenses to Common Shareholders associated with the Fund’s leverage. It is possible for the ARPS to be further downgraded in the future, possibly resulting in further increases to the maximum applicable rate and, thereby, the expenses borne by the Fund’s Common Shareholders.

Effective immediately, the first and second paragraphs of the “Fitch Preferred Shares Asset Coverage” section of the Prospectus are deleted and replaced with the following:

Satisfaction of Fitch Preferred Shares Asset Coverage requires that the Fund satisfy both a “Fitch Total Overcollateralization Test (“Fitch Total OC”) and a “Fitch Net Over Collateralization Test (“Fitch Net OC”), in each case to be consistent with the then-current rating assigned to the Preferred Shares by Fitch pursuant to the Fitch Criteria (as defined below). Under the Bylaws, Fitch Preferred Shares Asset Coverage is satisfied if, as of a particular date or time, the Fund has sufficient asset coverage with respect to the Preferred Shares such that the Fund satisfies both the (i) Fitch Total OC test and the (ii) Fitch Net OC test as of such date or time. The Fitch Total OC test and the Fitch Net OC test are satisfied if the Fund has Fitch Total OC or Fitch Net OC, as the case may be, in excess of one-hundred percent (100%) pursuant to the applicable formula below.

The Fund’s Bylaws incorporate by reference the report issued by Fitch Ratings entitled “Closed-End Funds and Market Value Structures Rating Criteria” or similar future report(s) regarding closed-end fund rating criteria

most recently published by Fitch and approved for use by the Fund by resolution of the Board of Trustees of the Fund (the “Fitch Criteria”). The Fitch Criteria include, among other things, the current formulations for satisfaction of the Fitch Total OC test and the Fitch Net OC test, asset discount factors (used in part to calculate Fitch Total OC and Fitch Net OC), issuer and industry diversification and concentration thresholds and guidelines and a description of other rating considerations.

Effective immediately, the fifth paragraph of the “Use of Leverage” section of the Prospectus is deleted and replaced with the following:

Regarding the costs associated with the Fund’s ARPS, the terms of the ARPS provide that they would ordinarily pay dividends at a rate set at auctions held every seven days, normally payable on the first business day following the end of the rate period, subject to a maximum applicable rate calculated as a function of the ARPS’ then-current rating and a reference interest rate as described below. However, the weekly auctions for the ARPS, as well as auctions for similar preferred shares of other closed-end funds in the U.S., have failed since February 2008, and the dividend rates on the ARPS since that time have been paid at the maximum applicable rate (i.e., the greater of a multiple of or a spread plus a reference rate, which is the greater of the applicable LIBOR rate or the applicable Treasury Index Rate). In September 2011, Moody’s, a ratings agency that provides ratings for the Fund’s ARPS, downgraded its rating of the ARPS from “Aaa” to “Aa2,” citing what it believed to be persistently thin asset coverage levels, increased NAV volatility and concerns about secondary market liquidity for some assets supporting rated obligations. In July 2012, Moody’s downgraded its rating of the ARPS from “Aa2” to “Aa3” pursuant to a revised ratings methodology adopted by Moody’s. In May 2020, Fitch downgraded its rating of the ARPS from “AAA” to “AA,” indicating the downgrades reflected recent extreme market volatility and reduced asset liquidity, which it believed had quickly eroded asset coverage cushions for closed-end funds and challenged fund managers’ ability to deleverage. On December 4, 2020, Fitch published ratings criteria relating to closed-end fund obligations, including preferred shares, which effectively result in a rating cap of “AA” for debt and preferred stock issued by closed-end funds and a rating cap of “A” for (i) debt and preferred shares issued by closed-end funds exposed to corporate debt, emerging market debt, below-investment-grade and unrated debt, structured securities and equity, (ii) and closed-end funds with material exposure to “BBB” category rated assets. Following the close of business on April 30, 2021, Fitch downgraded its rating of the ARPS from “AA” to “A” pursuant to the revised ratings methodology and related new rating caps. See “Use of Leverage” and “Description of Capital Structure.” The Fund expects that the ARPS will continue to pay dividends at the maximum applicable rate for the foreseeable future and cannot predict whether or when the auction markets for the ARPS may resume normal functioning. See “Principal Risks of the Fund—Leverage Risk,” “Principal Risks of the Fund—Additional Risks Associated with the Fund’s Preferred Shares” and “Description of Capital Structure” for more information.

Effective immediately, the fifth paragraph of the “Investment Objectives and Policies – Leverage and Borrowing” section of the SAI is deleted and replaced with the following:

Regarding the costs associated with the Fund’s Preferred Shares, the terms of the ARPS provide that they would ordinarily pay dividends at a rate set at auctions held every seven days, normally payable on the first business day following the end of the rate period, subject to a maximum applicable rate calculated as a function of the ARPS’ then-current rating and a reference interest rate, as described below. However, the weekly auctions for the ARPS, as well as auctions for similar preferred shares of other closed-end funds in the U.S., have failed since February 2008, and the dividend rates on the ARPS since that time have been paid at the maximum applicable rate (i.e. the greater of a multiple of or a spread plus a reference rate, which is the greater of the applicable LIBOR rate or the applicable Treasury Index Rate). In September 2011, Moody’s, a ratings agency that provides ratings for the Fund’s ARPS, downgraded its rating of the ARPS from “Aaa” to “Aa2,” citing what it believed to be persistently thin asset coverage levels, increased NAV volatility and concerns about secondary market liquidity for some assets supporting rated obligations. In July 2012, Moody’s downgraded its rating of the ARPS from “Aa2” to “Aa3” pursuant to a revised ratings methodology adopted by Moody’s. See “Description of Capital Structure.” Under the Fund’s amended and restated bylaws (the “Bylaws”), the 2011 downgrade resulted in an increase in the dividend rate multiplier from 1.25 to 1.50, thereby increasing the dividend rate payable to ARPS holders and increasing the expenses to Common Shareholders associated with the Fund’s leverage. In May

2020, Fitch downgraded its rating of the ARPS from “AAA” to “AA,” indicating the downgrades reflected recent extreme market volatility and reduced asset liquidity, which it believed had quickly eroded asset coverage cushions for closed-end funds and challenged fund managers’ ability to deleverage. Under the Bylaws, the 2020 Fitch downgrade resulted in an increase in the applicable spread over the reference rate from 125 bps to 150 bps, thereby increasing the dividend rate payable to ARPS holders and increasing the costs to Common Shareholders associated with the Fund’s leverage. On December 4, 2020, Fitch published ratings criteria relating to closed-end fund obligations, including preferred shares, which effectively result in a rating cap of “AA” for debt and preferred stock issued by closed-end funds and a rating cap of “A” for (i) debt and preferred shares issued by closed-end funds exposed to corporate debt, emerging market debt, below-investment-grade and unrated debt, structured securities and equity, (ii) and closed-end funds with material exposure to “BBB” category rated assets. Following the close of business on April 30, 2021, Fitch downgraded its rating of the ARPS from “AA” to “A” pursuant to the revised ratings methodology and related new rating caps. Under the Bylaws, the April 2021 Fitch downgrade resulted in an increase in the dividend rate multiplier from 1.50 to 2.00, which could increase the dividend rate payable to ARPS holders should the maximum dividend rate be determined via the multiplier in lieu of the spread noted above (the maximum dividend rate is based on the greater of a multiple of or a spread plus a reference rate) and, thereby, increase the expenses to Common Shareholders associated with the Fund’s leverage.    See “Use of Leverage” and “Description of Capital Structure.” The Fund expects that the ARPS will continue to pay dividends at the maximum applicable rate for the foreseeable future and cannot predict whether or when the auction markets for the ARPS may resume normal functioning. See “Principal Risks of the Fund—Leverage Risk,” “Principal Risks of the Fund—Additional Risks Associated with the Fund’s Preferred Shares” and “Description of Capital Structure” in the Prospectus for more information.

Investors Should Retain This Supplement for Future Reference

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