A cooling apparatus for an internal combustion engine includes a pump, a radiator, a flow rate adjustment valve, a bypass passage, and a controller. The flow rate adjustment valve includes a valve member that rotates to change an open degree of the flow rate adjustment valve and a valve member biasing component that biases the valve member in a valve-closing direction in which the open degree decreases. The valve member rotates in a valve-opening direction in which the open degree increases when a pressure difference increases between positions upstream and downstream of the valve member in a flow direction of coolant in the circulation circuit and rotate in the valve-closing direction when the pressure difference decreases. The controller increases the pump discharge amount as a target radiator flow rate that is a target of an amount of coolant passing through the radiator increases.