To restrain a torque shock, and to improve startability when automatically starting an internal combustion engine after automatically stopping the internal combustion engine.

After motoring the engine up to an idle speed by a motor generator, an initial value of an inertia torque conversion flow rate Qmg as an air flow rate equivalent to an inertia torque quantity of a rotary system on a crankshaft 26 and its damping factor are set based on a shift position SP and a water temperature Tw of cooling water of the engine (S140 and 150). The engine is controlled for starting by using an idle speed maintaining flow rate Qiscc obtained by subtracting the inertia torque conversion flow rate Qmg calculated thereby from a target idle speed Qisc* (S180 to S200). As a result, the torque shock can be restrained when automatically starting the engine.