A clutch water pump may include a pulley, a brake pad attached on an interior surface of the clutch compartment of the pulley, a clutch disk disposed corresponding to the brake pad in the clutch compartment, a hub rotatably mounted into the penetrating hole and coupled to the clutch disk through a plurality of spring pins, the plurality of spring pins connecting slidably the clutch disk to the hub, a magnetic actuator fixed to the hub and disposed to the clutch disk to selectively move the clutch disk toward or away from the brake pad, and a main shaft, one end of which is fixed to the center of the hub and the other end of which is fixed to an impeller. Furthermore, a method of controlling the clutch water pump according to the engine rotation speed, the coolant temperature, and a condition of the coolant temperature sensor is provided.