Giambattista Grossi was born in Mantua to a noble family. His mother was the sister of Giorgio Andreasi, who later became bishop of Reggio Emilia. Gianbattista followed in his uncle's footsteps and became dean of the chapter.[2]
On 4 December 1545, Giambattista Grossi was appointed during the papacy of Pope Paul III as Coadjutor Bishop of Reggio Emilia, because his uncle was quite old and ill.[3] On 22 January 1549 Giorgio Andreasi died and he succeeded to the bishopric.[1] On 5 May 1549 Giambattista Grossi was consecrated as bishop in the Reggio Emilia Cathedral by Gian Pietro Ferretti.[3]
In 1551 and 1552, and later in 1564, he participated to the Council of Trent. In 1558, he issued a constitution promoting a temperate lifestyle among the clergy and providing guidance for parish priests in their pastoral responsibilities (De vita et honestade Clericorum).[4] In October 1565 he published in the Cathedral the decrees of the Council of Trent. He established the Seminary as well, levying a tax on all ecclesiastical benefices to support its foundation.[4]
He served as Bishop of Reggio Emilia until his death on 28 March 1569.[3] He was buried in that cathedral.[2]