Linton Deck Jr., superintendent of the Fairfax County school system--the nation's 11th largest--resigned last night after harsh disagreements with the county school board.

Deck's sudden resignation at the close of a board meeting in Fairfax City followed an annual review of his performance. Over the 2 1/2 years he has held the job, some board members have been highly critical of what they have called his abrasive personality and poor image with community organizations.

"The board and the superintendent have concluded that they have divergent and mismatching views with respect to the manner of conducting the business of the Fairfax school system," the board and Deck said in a joint statement read by Board Chairman Ann P. Kahn following an executive (closed) board session. Deck remained silent. Members of his staff, some of them with tears in their eyes, hugged him and pumped his hand as he left the room.

Sources close to the board said Deck, 53, agreed to resign after being pressured by board members dissatisfied with his leadership. His resignation is effective July 16, but he will remain as an employe of the school system until Oct. 31 to assist in the transition to a new administration.

He has been paid almost $70,000 a year, including expenses and benefits, and the board agreed to pay him $75,000 for his contract, which would not expire for another 2 1/2 years.

Deputy superintendent William J. Burkholder was named acting superintendent, a role he filled for several months before Deck arrived in early 1980.

Deck's superintendency has been tumultuous. He was criticized early in his administration for his handling of school closings and principal transfers, and other criticisms have been mounting for the past year among some board members and teacher and parent groups.

The Fairfax Education Association, the county's largest teachers group, censured him in January for what it called mishandling of school closings on a snowy day when many buses were unable to reach the schools and thousands of students were left stranded.

He encountered board criticism for submitting a budget proposal several weeks ago that some members called excessive at a time when most Washington-area governments were cutting expenditures.

But he had his supporters. While some board members criticized him for expanding the use of computers in classrooms and administrative offices, others hailed it as a major achievement.

While many were critical of what they perceived as arrogance and an overbearing personality, others praised his managerial skills.

The board's vote to accept Deck's resignation was 8 to 2, with members Carmin Caputo and James W. Kitchen dissenting. Caputo said later he didn't agree with the majority that Deck's and the board's views differed sufficiently to warrant resignation.

Other board members and Deck declined to comment on the resignation beyond the joint statement.

Board spokesman George Hamel said some board members who voted with the majority "probably disagreed with the resignation, but may have voted for it because they were tired of all the turmoil surrounding him."

Deck left the Orlando, Fla., school system to accept the Fairfax job several months after receiving a "no confidence" vote from the school board there.

Some members of the school boards in both Orlando and Fairfax eventually came to believe Deck was injecting his own philosophies and objectives into the school system, rather than those expressed by the community and the board.