Pietro Costa spent his youth in Florence. He was a sculptor as well as a painter of historical figures, still lifes and street scenes. Upon obtaining a pension he went to Rome where he could study more seriously. He won a prize in the competition held for the erection of a monument to Victor-Emmanuel in Turin.
While still young he was chosen by his master, Garzzarini to erect a colossal statue of Christopher Columbus. Some time afterwards he was entrusted to erect a stuste of Francesco Redi which upon completion was placed in a niches at the Uffizzi in Florence. Costa later is his career was active as a teacher at the academy of fine arts in Genoa.