Disclosed is an engine driving system having a cell suitable for restarting an engine, wherein an engine is stopped at the time of stopping running of a vehicle and the engine is restarted at the time of starting running of the vehicle, there are provided an engine electronic control device for controlling the engine, a motor for restarting the engine and a cell for supplying an electrical power to the motor; the cell comprises an anode plate formed into a thin band-shape, a cathode plate formed into a thin band-shape and a band-like separator arranged between the anode plate and the cathode plate; and the anode plate, the cathode plate and the separator form a group of wound pole plates and the group of pole plates is immersed in electrolysis solution.