To crank an internal combustion engine while preventing over discharge of a storage device and suppress vibration at a time of start.

When a transmission is shifted to P range, or vehicle speed V is 0 or demand torque Tr* demanded on a drive shaft is 0 or more, after engine start is demanded, power from a battery is supplied and a motor is driven to start engine cranking, a start device for the internal combustion engine establishes rotation speed Nm1* after adjustment having hysteresis on change in motor rotation speed reduction side during engine cranking (S330-S370), establishes adjustment torque Tα based on the established rotation speed Nm1* after adjustment and output limit Wout of the battery (S390), and adjust motor cranking torque by adjustment torque Tα. Consequently, vibration at a time of engine cranking can be suppressed while preventing over discharge of the battery.