The Defense Department's chief spokesman, Robert B. Sims, announced yesterday that he is stepping down to assume a new post as vice president for communications of the National Geographic Society.

Sims, 53, will leave the Pentagon Sept. 20 after 13 years as a Washington public information officer, including almost two years as assistant secretary of defense for public affairs.

Sims said he was departing the Reagan administration for "personal reasons" and is "leaving in full support of their {the administration's} policies."

No successor has been named, according to Sims.

His announcement concluded a special news briefing yesterday afternoon on the status of the Navy's escorting mission for three reflagged Kuwaiti oil tankers through the Persian Gulf. Sims had just finished responding to a battery of questions from reporters irate that some Pentagon sources had informed them -- the day before the Navy moved ahead with the second convoy into the gulf -- that the operation had been delayed for up to a week.

After lecturing reporters on the importance of maintaining security of the mission's operational details, Sims said, "I have never knowingly lied to you."

The National Geographic Society said yesterday that the position to be occupied by Sims is a new job designed in part to help the organization celebrate its 1988 centennial and "continue its vigorous campaign to improve geography education."

In accepting Sims' resignation, Defense Secretary Caspar W. Weinberger praised his chief spokesman, noting that under Sims "military-media relations have improved significantly."

Weinberger cited Sims "on the successful implementation of the department's media-pool concept, ensuring that news organizations working with us have a better means of covering and reporting military activities to the American people."

The pool was most recently used two weeks ago on the first U.S. Navy escorting mission into the Persian Gulf, and again last week on that convoy's return trip out of the gulf.

Sims began his public affairs career as special assistant to the Navy secretaries from 1974-78 before serving as deputy chief of information for the department from 1978-81.

He then became senior director of public affairs for the National Security Council and later served as White House deputy secretary for foreign affairs before moving to the Pentagon in October 1985.

Sims and his wife, Patricia, live in Georgetown. The couple has four children. He is a native of Alamo, Tenn., and has a master's degree in journalism and political science from the University of Wisconsin at Madison.