A cooling apparatus for a power-pack in a hybrid vehicle may include a power-pack that acquires traveling information of the vehicle and controls the operation of an engine and a motor, a low-temperature radiator that is connected with power-pack through a cooling water channel, dissipates heat from the cooling water discharged from power-pack, and is arranged in parallel with a radiator, and an electric water pump that is disposed in the cooling water channel and operated in response to an electric signal output from an ECU to circulate the cooling water through power-pack and low-temperature radiator. The cooling apparatus may also include a cooling fan. A cooling method of using the cooling apparatus may include determining engine operation, determining start of a water pump, and operating a water pump. The cooling method may also include starting a cooling fan, operating a cooling and examining a water pump.