Avraham was born in 1919 in Zofiówka, Poland, to Benzion and Zeitel Steinberg, landowning farmers who were religiously observant. His mother died when he was fourteen, while his two brothers and father perished later in the Holocaust.
Avraham studied in cheder from age five; at age eight, he started studying with a private tutor as well. In 1935, he joined Beitar; IZL, in 1937. Under the auspices of the latter, he attended a course in Zofiówka in 1939; in August of that year, he joined the Revisionist Af al Pi program. His group was stuck at the border of Poland and Romania for two weeks, then sent home. However, it was clear to them that they had to try again. The outbreak of World War II and the Russian advance into eastern Poland offered them the opportunity. After various attempts to cross the border (twice resulting in arrest), they finally made it to Vilnius.
In early 1941, Avraham got permission through the Irgun to make aliyah, using a forged letter from the British Consulate. Finally, on 31.3.1941, he made it to the Promised Land.
He was arrested and sent to Atlit; while there, he made contact with Lehi. After about a year, he was released, and he immediately joined Lehi.
Avraham, the Ginger (as his friends called him), began working in the armory, under Eliyahu Korev, who taught him how to arrange the magazines. He also put up posters and provided security for those doing so. He helped transport and find refuge for the twenty men who fled from Latrun. He also was part of the attack on the High Commissioner, as well as the planning and execution of other operations.
Late in August 1944, he was arrested and exiled to Africa with the first group of 251. He was part of the planning and execution of various escape schemes, including digging tunnels and the great escape in Eritrea of 54 detainees. However, on 29.6.1946, he was captured with others and returned to the camp. When they were transferred to Gilgil in Kenya, he planned more escapes. After the establishment of the State, he started a hunger strike with four others, demanding their immediate return to Israel. Once he heard from the camp commander that they would be sent home within 36 hours, he ended the strike. They returned on 12.7.1948.
The Lehi Central Committee sent him to Jerusalem, where he served in Talbiyeh, under Yehoshua Zattler. After the Bernadotte assassination, he had to flee to escape arrest. A few months later, he was able to join the IDF.
In the summer of 1949, he was discharged, and he joined the Neve Yair settlement in the Negev. He served as the regional commander as long as the settlement existed, and he returned to the city when it was disbanded. He worked in construction as a work supervisor for many years, even past retirement age.
Avraham and his wife, Rivkaleh née Shabtai, had twin boys, Benzion and Yosef.