Born Haim Finkel in Odessa in the Russian Empire (today in Ukraine), Ben-Asher studied at a heder.

A member of the Ein Harod platoon in the city, he was amongst the founders of kibbutz Givat Brenner in 1928, although he later moved to Netzer Sereni after the split in the HaKibbutz HaMeuhad movement.

Whilst in the army, he edited The Soldier newspaper and the Jewish Bridage's magazine, HaMa'avak.

A member of Mapai's central committee, in the first Knesset elections in 1949 he won a seat on the party's list.

Ben-Asher also served as director of Beit Berl Academic College.