A cooling apparatus of a vehicle driving system for driving a vehicle, comprising: an engine water circulation passage, in which engine cooling water flows for cooling an internal combustion engine of the vehicle driving system; an engine radiator for cooling the engine cooling water by outside air; a hybrid system water circulation passage, in which hybrid system cooling water flows for cooling a hybrid system including at least one of a battery and a motor (111, 112) of the vehicle driving system; a hybrid system radiator for cooling the hybrid system cooling water by the outside air; and a heat pump for cooling the hybrid system with a cooling medium, the heat pump including a condenser for exchanging heat between the cooling medium and the engine cooling water, wherein the cooling apparatus further comprises an electronic control unit configured to: flow the engine cooling water in the engine water circulation passage through the engine radiator to cool the internal combustion engine with the engine cooling water when an engine cooling condition is satisfied, the engine cooling condition being a condition that a process of cooling the internal combustion engine with the engine cooling water is requested; activate the heat pump to cool the hybrid system with the cooling medium when a heat pump activation condition is satisfied, the heat pump activation condition being a condition that a process of cooling the hybrid system with the cooling medium of the heat pump is requested; and activate the heat pump to cool the hybrid system with the cooling medium and flow the engine cooling water in the engine water circulation passage through the condenser to cool the cooling medium with the engine cooling water at the condenser when an engine water circulation condition is satisfied, the engine water circulation condition being a condition that the heat pump activation condition is satisfied, and the engine cooling condition is not satisfied characterized in that the heat pump is configured to cool the hybrid system directly by the cooling medium. an engine water circulation passage, in which engine cooling water flows for cooling an internal combustion engine of the vehicle driving system; an engine radiator for cooling the engine cooling water by outside air; a hybrid system water circulation passage, in which hybrid system cooling water flows for cooling a hybrid system including at least one of a battery and a motor (111, 112) of the vehicle driving system; a hybrid system radiator for cooling the hybrid system cooling water by the outside air; and a heat pump for cooling the hybrid system with a cooling medium, the heat pump including a condenser for exchanging heat between the cooling medium and the engine cooling water, wherein the cooling apparatus further comprises an electronic control unit configured to: flow the engine cooling water in the engine water circulation passage through the engine radiator to cool the internal combustion engine with the engine cooling water when an engine cooling condition is satisfied, the engine cooling condition being a condition that a process of cooling the internal combustion engine with the engine cooling water is requested; activate the heat pump to cool the hybrid system with the cooling medium when a heat pump activation condition is satisfied, the heat pump activation condition being a condition that a process of cooling the hybrid system with the cooling medium of the heat pump is requested; and activate the heat pump to cool the hybrid system with the cooling medium and flow the engine cooling water in the engine water circulation passage through the condenser to cool the cooling medium with the engine cooling water at the condenser when an engine water circulation condition is satisfied, the engine water circulation condition being a condition that the heat pump activation condition is satisfied, and the engine cooling condition is not satisfied flow the engine cooling water in the engine water circulation passage through the engine radiator to cool the internal combustion engine with the engine cooling water when an engine cooling condition is satisfied, the engine cooling condition being a condition that a process of cooling the internal combustion engine with the engine cooling water is requested; activate the heat pump to cool the hybrid system with the cooling medium when a heat pump activation condition is satisfied, the heat pump activation condition being a condition that a process of cooling the hybrid system with the cooling medium of the heat pump is requested; and activate the heat pump to cool the hybrid system with the cooling medium and flow the engine cooling water in the engine water circulation passage through the condenser to cool the cooling medium with the engine cooling water at the condenser when an engine water circulation condition is satisfied, the engine water circulation condition being a condition that the heat pump activation condition is satisfied, and the engine cooling condition is not satisfied characterized in that the heat pump is configured to cool the hybrid system directly by the cooling medium.