To effectively reduce start shock by slip control of the variable speed friction element with the highest effect on an output torque by transmission torque capacity control among variable speed friction elements of fastening conditions.

A hybrid vehicle is assumed, in which coupling between an engine and a motor/generator of a tandem arrangement is enabled with a first clutch, and which diverts the variable speed friction element in an automatic transmission as a second clutch which manages connect/disconnect between these both by making the automatic transmission intervene between the motor/generator and the driving wheel. When performing engine start by deterioration of transmission torque capacity of the second clutch and fastening of the first clutch, the variable speed friction element with the highest effect on the output torque by transmission torque capacity control is diverted to the second clutch (S23), and engine start shock is effectively reduced by the transmission torque capacity deterioration (slip) control (S25).