He obtained a doctorate degree in utroque iure at the University of Bologna, and began to teach civil and canon law there in 1611.

Returning to Rome in 1635, he was named councilor of the Roman Inquisition, the final court of appeal in trials of heresy; and in 1636 referendary of the Apostolic Signatura.

In 1653, he composed for Pope Innocent X the Cum occasione, a papal bull, condemning five propositions of Cornelius Jansen's Augustinus.

He wrote De inconstantia in jure admittenda vel non which described the increased standards of evidence and proof required by the Roman Inquisition in cases of alleged witchcraft.

Albizzi did not approve of the theories of Miguel de Molinos because, among other objections, it appeared to encourage the rejection of vocal prayer and the sacrament of confession, as had been seen in some convents of religious women.