Grammatica was born in either Siena or Rome. According to Giovanni Baglione the artist was given the name Antiveduto ("foreseen") because his father had a premonition that he would be soon be born during a journey between his native Siena and Rome. It was in Rome that Antiveduto was baptised, raised and based his career. His apprenticeship with the Perugian artist Giovanni Domenico Angelini (Giandomenico Perugino) introduced him to small-scale work, mostly on copper. He gained the nickname "gran Capocciante" because he specialised in painting heads of famous men. A decade later, in 1591, Antiveduto set up as an independent artist.
Grammatica's earliest surviving public commission, an old-fashioned configuration depicting Christ the Saviour with St. Stanislaus of Krakow, St. Adalbert of Prague and St. Hyacinth Odrowaz, was painted for the high altar of San Stanislao dei Polacchi. Characterized by Giulio Mancini as most zealous in his profession, Antiveduto began his association with the Accademia di San Luca in 1593. He gained great familiarity with the two protectors of the Academy, Cardinals Federico Borromeo and Francesco Maria Del Monte, and was closely attached to the latter; so much that he was elected to the highest office of the association as "principe" in 1624. Shortly after this, however, he became embroiled in scandal. The machinations of Grammatica’s enemy Tommaso Salini over the attempt to sell off the Accademia's altarpiece, thought to be by Raphael, brought about a humiliating retreat, when Cardinal Del Monte intervened to re-establish the constitution of the institution. His fortunes were in a way linked with the Cardinal himself, who was much frowned upon by the Barberini, and his death preceded that of Del Monte by four months, in April 1626.
- Gianni Papi, Antiveduto Grammatica, Soncino 1995
- Helmut Philipp Riedl, Antiveduto della Grammatica (1570/1-1626) Lebun und Werk, Berlin 1998
- Antonella Triponi, Antiveduto Grammatica. Una disputa del primo Seicento romano: nuovi documenti Storia dell'Arte 103
- Gianni Papi, Aggiornamenti per Antiveduto Gramatica, Arte Cristinana Marzo-Aprile 2003, 815 pp. 117–124
- Massimo Pulini, Il fossombrone ritrattista degli oratoriani. La racolta Mattei e Antiveduto Gramatica Paragone Marzo 2005 pp. 31–39
- Lione, Pascoli (1732). Vite de pittori, scultori, ed architetti Perugini. Antonio de' Rossi, Strada del Seminario Romano, Rome. p. 133.