It was founded in 1523 following permission from cardinal Domenico Grimani.  It enriched the Serenissima with marbles and ancient bronzes, the museum is based on donations from great Venetian families. 
Besides numerous Greek sculptures, it includes architecture and sculpture Roman fragments, epigraphs, marbles and busts, little bronzes, ceramics, jewellery, objects of roman, Tuscan and Mesopotamic origins, gems, ivories and a numismatic collection (with coins of the republican age from the III to the I century B.C.). 
Great importance is also given to Roman emperors’ portraits.

The publicly owned museum also contains a part of the archaeological collection of Museo Correr, including antiquities from the Neolithic age, Egyptian, Assyro-Babylonian, Greek, Tuscan, and Roman.