GOLDMAN SACHS VARIABLE INSURANCE TRUST

Goldman Sachs Core Fixed Income Fund

(the “Fund”)

Supplement dated October 2, 2018, to the

Summary Prospectuses, Prospectuses and Statement of Additional Information (the “SAI”),

each dated April 30, 2018, as supplemented to date

Jonathan Beinner will be retiring from Goldman Sachs on March 31, 2019. As a result, effective January 1, 2019 (the “Effective Date”) Mr. Beinner will no longer serve as a portfolio manager for the Fund. In addition, on the Effective Date, Ashish Shah will serve as a portfolio manager for the Fund.

Michael Swell, Managing Director, will continue to serve as a portfolio manager for the Fund.

Accordingly, on the Effective Date, the Fund’s disclosures are modified as follows:

All references to Mr. Beinner in the Summary Prospectuses, Prospectuses and SAI will be deleted in their entirety.

On the Effective Date, the following replaces in its entirety the “Portfolio Managers” subsection of the “Goldman Sachs Core Fixed Income Fund—Summary—Portfolio Management” section of the Prospectuses and the “Portfolio Management” section of the Summary Prospectuses:

Portfolio Managers: Ashish Shah, Managing Director, Co-Chief Investment Officer of Global Fixed Income, has managed the Fund since 2019; and Michael Swell, Managing Director, Co-Head Global Lead Portfolio Management, has managed the Fund since 2009.

On the Effective Date, the following row is added to the table in the “Fixed Income Portfolio Management Team” subsection of the “Service Providers—Fund Managers” section of the Prospectuses:

Ashish Shah, Managing Director, Co-Chief Investment Officer, Global Fixed Income Portfolio Manager— Core Fixed Income Since
2019 Mr. Shah is Co-Chief Investment Officer of Global Fixed Income, Global Head of Corporate Credit and Head of the Cross-Sector Strategy within Fixed Income. Mr. Shah joined the Investment Adviser in 2018. Mr. Shah was previously at AllianceBernstein from 2010 to 2018, where he was most recently the Head of Fixed Income and Chief Investment Officer of Global Credit.

This Supplement should be retained with your Prospectuses, Summary Prospectuses and SAI for future reference.

VITCFICONFIDSTK 10-18