Princess Anna was born in 1730 into one of the leading noble houses of Imereti, a kingdom in western Georgia. Her father was Prince Zaal Abashidze. Anna had two brothers, Ioane and Simon. The former served as a governor ("mouravi") of Borchalo and a chief of royal guards ("kechikchibashi") from 1769 to 1799 and saw action against the Persians at Krtsanisi in 1795. The latter was a keeper of the royal seal ("mordali").