An acid/alkaline hybrid resonance battery device with damping function is formed of a plurality of similar battery cells connected in either series or parallel. Every battery cell includes an acid rechargeable cell unit and an alkaline rechargeable cell unit, which are electrically connected in parallel. The acid rechargeable cell unit includes at least one acid rechargeable cell, and the alkaline rechargeable cell unit includes at least two serially connected alkaline rechargeable cells. The acid rechargeable cell unit has an electric potential and a capacity close to or equal to those of the alkaline rechargeable cell unit, so that a resonance damping effect is produced between the acid rechargeable cell unit and the alkaline rechargeable cell unit.