A. Jack Winston, 68, the founder and president of his own floor contracting firm, died Sunday at Georgetown University Hospital following a heart attack.

Mr. Winston was born in Macon, Ga., and earned undergraduate and business degrees at the University of Georgia. He was a certified public accountant.

He moved to the Washington area in the mid-1930s and went to work for Quaker City Linoleum, a flooring company of which he was vice president. In the late 1940s, he started his own firm, District Tile & Linoleum Co., Inc., and continued as its president until his death.

He was a member of the board of directors of the Washington Board of Trade. He also was a member of the Washington Hebrew Congregation and the Woodmont Country Club.

During World War II, Mr. Winston was a captain in the Army.

Survivors include his wife, Adele, of the homes in Washington and West Palm Beach, Fla.; three daughters, Sherry Bindeman Schwartz, of Philadelphia and Jane Winston and Carole Wilson, both of Washington; two brothers, Julius, of Arlington, and Sidney, of Adelphi; three sisters, Mildred Korobov, of Virginia Beach, Va., Bea Marshall, of Macon, and Elaine Specvak, of Jacksonville, Fla., and two grandchildren.

The family suggests that expressions of sympathy be in the form of contributions to the American Heart Association.