A cooling apparatus of a vehicle driving system of the invention connects an engine water circulation passage to a hybrid system water circulation passage and flows cooling water in the engine water circulation passage and the hybrid system water circulation passage to cool a first hybrid system component by the cooling water cooled by an engine radiator and cool a second hybrid system component by the cooling water cooled by a hybrid system radiator when an engine cooling process is not requested, a first hybrid system cooling process is requested, a second hybrid system cooling process is requested, and a connection condition is satisfied. The connection condition is satisfied when the engine cooling process is not requested, and the cooling water flowing into the hybrid system water circulation passage from the engine water circulation passage, can cool the first hybrid system component.