He was born on the twentieth of Jumadi al-Awwal 1361 A.H. (1942) in Qom. His father was Ayatollah Hajj Sayyid Muhammad Muhaqqiq Damad, who was the son-in-law of Ayatollah Uzma Hajj Shaykh Abdul Karim Hairi.
Sayyid Ali completed his primary school in 1953 and in the same year he began to study the preliminary stage of Howzah studies and Arabic literature. While studying in the Howzah he was privately tutored in high school studies.
In 1960-61 after completing the pre-Kharij texts of Rasa’il and Makasib, Muqqiq Damad began the Kharij stage of his Howzah studies, while studying the book Kifayatul Usool (the last text of Pre-Kharij studies). He attended the Kharij stage lectures of Ayatollah Brujardi for six months. From 1961 onwards he attended the Kharij lectures of his father and Ayatollah Hajj Shaykh Murtada al-Hairi. During these years he also benefited from the Kharij lectures of the Grand Ayatollahs Khu’i, Gulpaygani, Mirza Hashim Amuli, Hajj Shaykh Husayn Hilli, and Hajj Sayyid Yahya al-Mudarris al-Yazdi.
When his father died in February 1969, he took up the responsibility of leading the congregational prayer of the Bazar Masjid in Qom. Along with that he also undertook some social activities such as establishing a Qardil Hasanah fund – an association for looking after and educating orphans, cheap co-operative houses for needy indigents, a mosque and a seminary called “al-Mahdi”, and a 200 bed hospital named “Waliyye `Asr”.
After the victory of the Iranian Revolution, al-Damad took up the responsibility of reviewing and compiling the judicial laws for which he established an office for the research and study of the judiciary system. The Judicial Research & Study Office established by al-Damad is an organization that works in collaboration with a group of the religious scholars, judges and expert lawyers.
Al-Damad was a member of the supreme administrative council of the Howzah in Qom from 1981 till 1991. He also taught at various levels of the Howzah studies and presently is teaching Fiqh and Usool at the Kharij stage.