Born Haim Finkel in Odessa in the Russian Empire (today in Ukraine), Ben-Asher studied at a heder. He made aliyah to Mandatory Palestine in 1924, and studied at the Hebrew University. 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. He also worked as an emissary of the HeHalutz movement in Germany and Poland. During World War II he enlisted in the Jewish Brigade. 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. He was re-elected in 1951, but lost his seat in the 1955 elections. In 1959 he published a book, The Future World of Yesterday. Ben-Asher also served as director of Beit Berl Academic College.

He died in 1998 at the age of 94.

• The personal papers of Haim Ben-Asher are kept at the Central Zionist Archives in Jerusalem. The notation of the record group is A292.
• Haim Ben-Asher on the Knesset website