Irvin Alan Kraft was born in Huntington, West Virginia, on November 20, 1921. He attended from Johns Hopkins University but interrupted his education to join the army. He qualified for the Army Specialized Training Program and volunteered to become a doctor, which meant completing two years of pre-medical courses in nine months. His unit studied at NYU School of Medicine and he completed his residency in psychiatry at Kingsbridge VA Hospital in New York City. After a second tour of duty in the Air Force, he received a fellowship in child psychiatry at Tulane University in 1954. He moved to Houston in 1957 to initiate a child psychiatry program at Baylor College of Medicine. He later joined the UT School of Public Health as a clinical professor of mental health.
Kraft was instrumental in founding the Texas Institute of Child Psychiatry in 1963. He worked with Denton Cooley in 1968 as a psychiatric consultant to the heart transplant team. He died May 30, 2010, and is buried at Emanu El Memorial Park.