An electric power generator having two water tanks, and two chambers movable up and down inside the two water tanks respectively in opposite directions. Each chamber has a top wall having an air outlet covered by a pressure valve, and a bottom wall having a plurality of apertures serving as both water inlets and outlets. An electric motor drivably connected to two chains from which the two chambers are hung respectively. Upper and lower electromagnetic holding devices provided at top and bottom of each water tank for holding or releasing the chambers. Continuous up and down movement of the two chambers in opposite directions by buoyancy and gravity alternately and continuously drives the electric motor to generate electric power. A method of generating electric power is also disclosed.