A vehicle hybrid system configured to be used in a vehicle including an engine installed thereto, the vehicle hybrid system comprising: a transmission mechanically coupled with the engine; a drive shaft mechanically coupled with the transmission; a rotation-transmitting part coupled with the drive shaft; a power connecting-disconnecting part coupled with the drive shaft via the rotation-transmitting part; a motor generator mechanically coupled with the power connecting-disconnecting part; a directional power transmission part for transmitting power in a direction from the motor generator to the engine to drive the engine and for not transmitting power in a direction from the engine to the motor generator to drive the motor generator; and a controller electrically coupled with the motor generator and the power connecting-disconnecting part, characterised in that the controller is configured to: when the vehicle is stopping and the engine is rotated to start, cause the motor generator to perform power running while the power connecting-disconnecting part is disengaged as to start the engine via the directional power transmission part and to drive the transmission to rotate the drive shaft via the directional power transmission part; cause the motor generator to perform a power running while engaging the power connecting-disconnecting part as to rotate the drive shaft via power connecting-disconnecting part to drive the vehicle; and, when the vehicle is decelerated, cause the motor generator to perform regeneration while engaging the power connecting-disconnecting part, and engage the power connecting-disconnecting part until a speed of the vehicle reaches a predetermined lower limit. a transmission mechanically coupled with the engine; a drive shaft mechanically coupled with the transmission; a rotation-transmitting part coupled with the drive shaft; a power connecting-disconnecting part coupled with the drive shaft via the rotation-transmitting part; a motor generator mechanically coupled with the power connecting-disconnecting part; a directional power transmission part for transmitting power in a direction from the motor generator to the engine to drive the engine and for not transmitting power in a direction from the engine to the motor generator to drive the motor generator; and a controller electrically coupled with the motor generator and the power connecting-disconnecting part, characterised in that the controller is configured to: when the vehicle is stopping and the engine is rotated to start, cause the motor generator to perform power running while the power connecting-disconnecting part is disengaged as to start the engine via the directional power transmission part and to drive the transmission to rotate the drive shaft via the directional power transmission part; cause the motor generator to perform a power running while engaging the power connecting-disconnecting part as to rotate the drive shaft via power connecting-disconnecting part to drive the vehicle; and, when the vehicle is decelerated, cause the motor generator to perform regeneration while engaging the power connecting-disconnecting part, and engage the power connecting-disconnecting part until a speed of the vehicle reaches a predetermined lower limit. when the vehicle is stopping and the engine is rotated to start, cause the motor generator to perform power running while the power connecting-disconnecting part is disengaged as to start the engine via the directional power transmission part and to drive the transmission to rotate the drive shaft via the directional power transmission part; cause the motor generator to perform a power running while engaging the power connecting-disconnecting part as to rotate the drive shaft via power connecting-disconnecting part to drive the vehicle; and, when the vehicle is decelerated, cause the motor generator to perform regeneration while engaging the power connecting-disconnecting part, and engage the power connecting-disconnecting part until a speed of the vehicle reaches a predetermined lower limit.