Leonard Baskin was born on 15 August 1922 in New Brunswick, New Jersey, the son of Rabbi Samuel Baskin and his second wife May Guss. In 1929 the family moved to Brooklyn where Samuel Baskin had obtained a post as Rabbi at Congregation B'nai Israel. In 1936 Leonard started to attend night school at the Educational Alliance on the Lower East Side, where he met sculptor Maurice Glickman. Baskin had his first exhibition at Glickman's studio in 1939 and in 1940 won an Honorable Mention for Sculpture in the Prix de Rome competition. After attending New York University, School of Architecture and Allied Arts, in 1941 Baskin won a scholarship to Yale University, School of Fine Arts. From 1943 to 1946, he served in the United States Navy, after which he resumed his education at the New School for Social Research.
In 1950 Baskin travelled to Paris and studied at the Academie de la Grande Chaumiere. In early 1951 he moved to Florence, where he enrolled at Academia di Belle Arte. Baskin returned to the U.S. in the spring of 1951, and later that year moved to Massachusetts, where he became an instructor in printmaking at the Worcester Art Museum. From 1953 to 1974 Baskin taught art at Smith College in Northampton, and later taught at Hampshire College in Amherst from 1984 until 1994. Throughout his teaching career he continued to produce his own sculpture and graphic arts at his studio in Leeds, and ran a small art press, Gehenna Press, which he had started at Yale in 1942. A fifty-year retrospective of Gehenna Press books toured the United States in 1992. Among his public works are the Holocaust Memorial sculpture on the site of the First Jewish Cemetery in Ann Arbor, Michigan, and a bas relief of Franklin D. Roosevelt's 1945 funeral procession, part of the FDR Memorial dedicated in 1997 in Washington, D.C.
Baskin was the recipient of numerous honors and awards, including the Special Medal of Merit of the American Institute of Graphic Arts in 1965, the Gold Medal of the National Academy of Arts and Letters in 1969, and the Gold Medal of the National Academy of Design. He died 3 June 2000.