He was born in Moscow, the son of Boris and Sophie Gourevitsch, who were Mensheviks who opposed the Bolshevik regime and went into exile in Berlin in 1923. They escaped from Nazi persecution into France in 1933 and then, in 1940, fled from Paris to the United States, where the family settled in Hoboken, New Jersey. Leon Gouré enlisted in the US Army and became a US citizen in 1943. He fought as an infantryman in World War II, before serving in counterintelligence and, after the war, interviewed Nazis and their collaborators who were held as prisoners. After his discharge he studied at New York University, graduating in 1947, and then received a master's degree from Columbia University in 1949. He joined the Rand Corporation in Washington, D.C. in 1954, transferring to the organization's offices in Santa Monica, California, in 1959. He received a doctorate in political science from Georgetown University in 1961. As an analyst at Rand, he began to develop his ideas on civil defense in the Soviet Union. In 1961, he wrote an influential report suggesting that the Soviet Union had massively increased their civil defense preparations so as to protect large numbers of people in the event of a nuclear war. His reports on the subject contributed to the expansion of civil defense measures in the US during the 1970s and 1980s. In 1973, he wrote that:
The fundamental Soviet view is that the better the USSR is prepared for war, the greater and more credible is its ability to deter its adversary from risking military confrontation. This is the main reason why Moscow categorically rejects any concept of security based on a balance of 'mutual assured destruction.'
He also advised President Lyndon Johnson's administration on the war in Vietnam. According to Malcolm Gladwell, writing in 2013, Gouré was "brilliant, charismatic, incredibly charming and absolutely ruthless". He established the Vietnam Motivation and Morale Project, and in 1964 lived for a period in Saigon where his staff were sent to interview Viet Cong combatants. His report concluded that the Viet Cong were demoralised and would surrender after further bombing; and he briefed leading military figures accordingly. His opinions were opposed by fellow analyst Konrad Kellen. Events proved Kellen to be right. But it was Gouré's analysis that influenced US policy for several years. Gouré joined the University of Miami in 1969, as director of Soviet studiesat the Center for Advanced International Studies. In 1980, he moved to consultancy firmScience Applications International Corp., where he remained until his retirement in 2004. A resident of Potomac, Maryland, he died in 2007 of congestive heart failure in Arlington at the age of 84. His books included The Siege of Leningrad and Civil Defense in the Soviet Union, both published in 1962. In 2009, his papers were acquired by the Hoover Institution at Stanford University.