Peter Marzio, 39, director of the Corcoran Gallery of Art since 1978, will leave Washington this fall to become director of the Museum of Fine Arts, Houston. No successor has been named.

The surprise announcement came from Houston yesterday after a special meeting of the museum's board of directors voted the appointment late Tuesday afternoon. Marzio will replace William Agee, who resigned in February.

The Corcoran was clearly unprepared for the announcement yesterday, though Marzio had phoned colleagues and trustees Tuesday night to tell them the news. According to Corcoran associate director Jane Livingston, the life trustees of the museum were aware that Marzio was being recruited by the Houston museum, but the announcement of the appointment still came as a "shock." The rest of the staff was variously "stunned" and "saddened."

Reached by phone in Philadelphia, where he was attending a meeting of the American Association of Museums, Marzio explained the move: "It's a bigger museum, a more diverse collection, and I think it's a logical step. But it's hard. I love the Corcoran, and have an almost spiritual affinity to it. You don't make those kinds of changes for the money.

"But I've been living in Washington since 1968, and I like Houston and it just looks very exciting to me. Their museum budget is almost three times that of the Corcoran, and with bigger institutions you get other things in scale to go with it.

"The hard part is that the Corcoran treated me like a king, and the trustees are my friends. It's been much more than a job. If they can continue to grow in the next four years as they have in the last four, it will be a splendid institution."

Back at the Corcoran, aides scurried for official statements, but to little avail. Reached in New York, trustee Gilbert Kinney said that the move "will be very hard on the Corcoran, but very good for Peter," and added that a search committee will be organized. "But we haven't done anything yet; we're scattered all over the place on vacation, and I don't think there's a life member of the board in town."

Marzio's directorship has been short--four years--but his accomplishments have been formidable. Annual attendance has grown from 85,000 to more than 500,000, and the endowment has grown from about $3 million to nearly $6 million, plus future pledges. The physical plant--including the roof and skylights--was a high priority, and has been vastly improved, in part with $2 million in gifts from Armand Hammer, a deal negotiated by Marzio. Hammer paid for the renovation of the auditorium in addition to making a gift that made it possible for the Corcoran to abolish the only museum admission fee in Washington. Marzio also demonstrated sensitivity to the community, bringing such exhibitions as "Treasures from Ancient Nigeria," which had the highest attendance in Corcoran history.

But best remembered of Marzio's accomplishments will no doubt be the installation of climate control--a dream for decades--now nearly complete. Marzio is also credited with unifying the Corcoran and the Corcoran School of Art into a cohesive unit. "There was all but an electric barbed-wire fence between them when I arrived," he said, though he hastened to add that it was the trustees, not he, who made all of the above possible.

In Marzio, the Corcoran seemed, at last, to have found a formula that worked, after years of groping and changing course. Serving chiefly as an administrator and fund-raiser, he left exhibitions and acquisitions decisions to his associate director Livingston and curator Edward Nygren. There was--and still is--some highly vocal controversy stemming from increasing pressure by local artists to have more exposure and influence within the museum. But overall, Marzio's stay at the Corcoran has been among the most stable and productive in recent memory.

In Houston, Marzio will be in charge of an encyclopedic collection, which reaches from ancient Greek sculpture to contemporary art, and is housed in a neoclassical structure to which a wing designed by Mies van der Rohe has been added. The museum also encompasses an art school that opened across the street in 1979, and a sculpture garden by Isamu Noguchi has been commissioned to link the two buildings. The Bayou Bend Collection of American decorative arts will also come under his aegis.

Marzio will be the second Corcoran director to take over a museum in Houston. Walter Hopps was recently appointed director of the Menil Collection there.