Giovanni was the son of a well-known mathematician, Andrea Argoli, and was born at Tagliacozzo in the Abruzzi.
At the age of fifteen he published a poem on the silkworm, Bombace e Seta (Rome, 1624).
Two years later, emulous of the reputation Marino had just gained with his Adone, the young Argoli is said to have shut himself in an apartment, where he was visited only by servants bringing his food, and in seven months, at the age of seventeen, produced his Endimione (Rome, 1626).
In 1632 he followed his father to Padua (where the latter was professor of mathematics), taking the doctorate in law.
In addition to his Italian verse, Argoli produced a number of poems in Latin, and several works on archaeology and philology.