An engine start using an electric motor during a vehicle travel is performed by increasing an output torque of the electric motor in a slip state where a second frictional engagement element 3 connecting the electric motor 1 and a driving wheel slips. A controller determines a requested acceleration amount from a depression amount of an accelerator pedal. When the requested acceleration amount is significant, a different torque increment characteristic is applied, compared to a case where the requested acceleration amount is not significant. Thus, the internal combustion engine starts in a high response depending on the requested acceleration amount input by the driver, thereby improving a vehicle acceleration response.