A new genus and species of anthropoid primate, Bahinia pondaungensis gen. et sp. nov., is described from the Yashe Kyitchaung locality in the Late Middle Eocene Pondaung Formation (Myanmar). It is related to Eosimias, but it is represented by more complete remains, including upper dentition with associated lower jaw fragment. It is interpreted as a new representative of the family Eosimiidae, which corresponds to the sister group of the Amphipithecidae and of all other anthropoids. Eosimiidae are now recorded from three distinct Middle Eocene localities in Asia, giving support to the hypothesis of an Asian origin of anthropoids.