Eberhard was the eldest son and successor of Arnulf the Bad, duke of Bavaria (907-937). His dukeship was short, however, for he was banished by King Otto the Great in 938.
In 933 or 934, he was offered the Iron Crown of Lombardy by supporters of Rudolph II of Burgundy, an opponent of Hugh of Arles, after his renunciation of all claims on the Italian throne. His campaign to Italy failed. In 935, he was designated by his father as his heir to the duchy, without the consent of the baronage. At about this time, Eberhard married Liutgard.
On his father's death, he succeeded without fanfare, but quickly came into conflict with Otto, who opposed the privileges won by Arnulf from his father, King Henry the Fowler. In two campaigns in 938, in spring and fall, Otto defeated Eberhard and banished him. In his place he appointed his uncle Berthold, duke of Carinthia. Eberhard's place of banishment and date of death are unknown. He may have died around 940 and may have fled to Hungary, even assisting the rebels of 953.