UNITED STATES

SECURITIES AND EXCHANGE COMMISSION

Washington, D.C. 20549

SCHEDULE 13D

UNDER THE SECURITIES EXCHANGE ACT OF 1934

(Amendment No. 1)*

Barnwell Industries, Inc.

(Name of Issuer)

Common Stock, par value $0.50 per share

(Title of Class of Securities)

068221100

(CUSIP Number)

Ned L. Sherwood

4731 North Highway A1A, Suite 213

Vero Beach, FL 32963

(772) 226-7923

(Name, Address and Telephone Number of Person Authorized to Receive Notices and Communications)

December 17, 2013

(Date of Event Which Requires Filing of This Statement)

If the filing person has previously filed a statement on Schedule 13G to report the acquisition that is the subject of this Schedule 13D, and is filing this schedule because of §§240.13d-1(e), 240.13d-1(f) or 240.13d-1(g), check the following box  ¨

Note: Schedules filed in paper format shall include a signed original and five copies of the schedule, including all exhibits. See §240.13d-7 for other parties to whom copies are to be sent.

The information required on the remainder of this cover page shall not be deemed to be “filed” for the purpose of Section 18 of the Securities Exchange Act of 1934 (“Act”) or otherwise subject to the liabilities of that section of the Act but shall be subject to all other provisions of the Act (however, see the Notes).

(Continued on following pages)

This Amendment No. 1 to Schedule 13D (this “Amendment No. 1”) relates to the common stock, par value $0.50 per share (the “Shares”), of Barnwell Industries, Inc., a Delaware corporation (the “Issuer”) and amends the Schedule 13D filed on June 11, 2013 (the “Original Schedule 13D” and, together with this Amendment No. 1, the “Schedule 13D”). Capitalized terms used and not defined in this Amendment No. 1 have the meanings set forth in the Original Schedule 13D. This Amendment No. 1 is being filed by Ned L. Sherwood (“Sherwood”) and MRMP-Managers LLC, a Delaware limited liability company (“MRMP” and together with Sherwood, the “Reporting Persons”).

This Amendment No. 1 is being filed to amend Item 4 and Item 7 of the Schedule 13D as follows:

Item 4 of the Schedule 13D is amended by adding thereto the following:

On December 17, 2013, Sherwood delivered a letter to the Issuer, a copy of which is attached hereto as Exhibit 4 and is incorporated in its entirety herein by reference. MRMP will also deliver a demand letter to the Issuer pursuant to Section 220 of the Delaware General Corporation Law, requesting the opportunity to inspect and make or receive copies of certain records of the Issuer (the “Demand Letter”). The form of the Demand Letter is attached hereto as Exhibit 5 and is incorporated in its entirety herein by reference.

Item 7 of the Schedule 13D is amended by adding thereto the following:

SIGNATURES

After reasonable inquiry and to the best of my knowledge and belief, I certify that the information set forth in this statement is true, complete and correct.

Exhibit 4

Ned L. Sherwood

4731 North Highway A1A, Suite 213

Vero Beach, FL 32963

Tel: (772) 226-7923

Fax: (772) 231-0207

December 17, 2013

The Board of Directors

Barnwell Industries

1100 Alakea Street, Suite 2900

Honolulu, HI 96813

To the Board:

As you know from my filings at the Securities and Exchange Commission, I am a long term shareholder of Barnwell Industries common stock. I own approximately 10.5% of the Company, and I am deeply concerned by the operations and governance of the Company.

In my last letter, dated June 11, 2013, I pointed out several disturbing practices at the Company and offered some suggestions on how to take immediate actions to stop the ongoing value destruction at the Company. For example, I believe that salaries should be reduced immediately in the C-suite and that any future pay should be linked to operating metrics and stock price performance. Furthermore, the Board should institute a mandatory retirement age in order to bring in new expertise and create some urgency for enhancing value to all shareholders. As I pointed out, the Board has overseen zero appreciation in nearly 25 years, and publicly available information strongly suggests that the Kinzlers are using this Company as their personal piggy bank.

My letter today is to voice my continued concern about the Company’s horrendous operational performance, its lack of even a semblance of good governance practices, and its disastrous stock performance.

Let’s start with the facts:

Now let’s look at some of what I believe are the reasons:

Now let’s look at the Company’s governance:

Finally, let us look at the Kinzlers’ family history of nepotism and what certainly appears to be their ongoing looting of the Company:

It has been several months since my initial Schedule 13D filing and letter. Just last week Barnwell reported horrible results again, and it appears there has been no positive changes to the operations. It seems as if the looting, nepotism, and ineffective corporate governance practices at the Company continue. The Board has a fiduciary duty to shareholders and, with six lawyers among the board members, there can no doubt the Board is well aware of the importance of their fiduciary duties. Nonetheless, the Board has been utterly complacent, if not completely complicit, in the Kinzler family’s complete mismanagement of the Company and destruction of shareholder value. I will be making a books and record request to explore more fully, among other things, the Board’s role in these troubling matters.

The horrible results of the Company speak for themselves. I believe the Board should now speak to shareholders and explain the following:

Many shareholders have communicated with me since my last letter, yet I see no action being taken. Here are some suggestions for the Board:

I plan to follow up this letter with a books and record request. Additionally, I urge all shareholders to write to the Board and request their individual resignations at a minimum. It is well past due for major changes at Barnwell.

Sincerely,

/s/ Ned L. Sherwood

Ned L. Sherwood

Exhibit 5

MRMP-Managers LLC

December     , 2013

Re: Demand for Inspection of Certain Records Pursuant to 8 Del. C. § 220

Dear Alexander and Russell:

MRMP-Managers LLC, a Delaware limited liability company (“MRMP”), is a stockholder of Barnwell Industries, Inc. (“Barnwell” and together with all of its subsidiaries, the “Company”). A true and correct copy of the Schedule 13D filed with the Securities and Exchange Commission by MRMP and Ned L. Sherwood on June 11, 2013 and Amendment No. 1 thereto filed on December 17, 2013, confirming MRMP’s beneficial ownership of 661,584.138 shares of common stock, $0.50 par value per share (the “Shares”), of Barnwell, is attached hereto as Exhibit A.

Pursuant to Section 220(b) of the Delaware General Corporation Law (the “DGCL”), MRMP is entitled to, and hereby demands the right, during the usual hours of business, to inspect the following records and documents of the Company and to make copies or extracts therefrom:

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The purposes of this demand are as follows:

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MRMP hereby designates and authorizes Adam Offenhartz and Eduardo Gallardo of Gibson, Dunn & Crutcher LLP and their respective partners, associates and any other person to be designated, acting together, singly or in combination, to conduct as its agents, the inspection and copying herein requested and to otherwise act on MRMP’s behalf, and MRMP has executed a Power of Attorney so providing, which is attached as Exhibit B hereto. MRMP is prepared to maintain appropriate confidentiality of the materials provided in response to this letter, and thus will enter into a reasonable confidentiality agreement in order to facilitate the inspection of the Company’s books and records and other materials. Additionally, MRMP will bear the reasonable costs incurred by the Company and its agents and representatives in connection with producing and furnishing the requested information.

Within five business days after the date of this letter, please have your counsel advise Mr. Offenhartz, to make arrangements for the inspection and copying of the aforementioned books, records and other documents. Mr. Offenhartz can be reached at 212-351-3808 (e-mail: aoffenhartz@gibsondunn.com). Alternatively, if the Company desires, it can provide the records herein demanded without the need for inspection and copying by MRMP’s agents by promptly sending complete and unredacted copies of them to Mr. Offenhartz.

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This demand is made under oath pursuant to Section 220 of the DGCL. The undersigned affirms the foregoing statements to be true to the fullest extent of its knowledge and belief under penalty of perjury under the laws of the United States of America.

Sworn to before me this day of December 2013

EXHIBIT A

(See attached)

EXHIBIT B

POWER OF ATTORNEY

KNOW ALL PERSONS BY THESE PRESENTS that the undersigned hereby constitutes, designates and appoints, Eduardo Gallardo, Adam Offenhartz and their respective partners, associates, employees and any other persons to be designated by any of them, acting together, singly or in combination, as such person’s true and lawful attorney-in-fact and agent for the undersigned and in the undersigned’s name, place and stead, in any and all capacities, to conduct the inspection and copying of the records demanded in the Demand for Inspection of Certain Records Pursuant to 8 Del. C. § 220, dated December         , 2013.

IN WITNESS WHEREOF, the undersigned has executed this instrument effective as of the          day of December, 2013.