Amjad Ali Khan was born in Gwalior on 9 October 1945 as Masoom Ali Khan, the youngest of seven children, to Gwalior court musician Hafiz Ali Khan and Rahat Jahan. His family is part of the Bangash lineage and Khan is in the sixth generation of musicians; his family claims to have invented the sarod. His personal name was changed by a sadhu to Amjad. Khan received homeschooling and studied music under his father. In 1957, a cultural organization in Delhi appointed Hafiz Ali Khan as its guest and the family moved to Delhi. Friends of Hafiz Ali convinced him of the importance of formal schooling for his son; as a result, Amjad was taken to meet the Principal of Modern School in New Delhi and admitted there as a day scholar. He attended Modern School from 1958 to 1963.
Khan first performed in the United States in 1963 and continued into the 2000s, with his sons. He has experimented with modifications to his instrument throughout his career. Khan played with the Hong Kong Philharmonic Orchestra and worked as a visiting professor at the University of New Mexico. His jugalbandhi with Bismillah Khan are worth hearing.