Born in Ferrara in 1460, he was influenced, possibly trained, by Ercole de' Roberti, the leading Ferrara painter of the Cosmè Tura painting school in the late 15th century. Costa was one of the first members of the Ferrara-Bologna School to adopt a soft and atmospheric style. 

In 1483, Costa probably settled in Bologna, where he worked until 1506, sporadically visiting Ferrara and Rome.  

Immediately after the expulsion of the Bentivoglio family from Bologna, in 1506, he was summoned to Mantua as court painter, to succeed Andrea Mantegna. 

He remained the city’s leading artist until the arrival of Giulio Romano in 1524, but little remains of his extensive work. His mature style often recalls that of Perugino, with a delicate sensitivity for landscapes; it has been suggested that he inspired Giorgione.  

His most ambitious works were the altarpieces created for churches in Bologna. These include his earliest dated work, the Bentivoglio altarpiece of 1488. Later works, such as the altarpiece in the Gallery, The Virgin and Child with Saints, are more influenced by Francia and Perugino. 

In 1506, he moved to Mantua as court painter, called by Isabella d'Este; here he was drawn to the art of Mantegna. 

Costa's last painting is The Enthroned Virgin and Saints for the Church of S. Silvestro signed and dated by the painter in 1525. This artwork represents a memorable synthesis of the artist’s last studies before his death in Mantua in 1535.