A device for controlling the rotation speed of a cooling fan of an internal combustion engine in a vehicle such as an automobile, wherein the fan is driven by a hydraulic motor powered by an operating fluid supplied by a pump directly driven by the engine, wherein the device controls partial relief of the hydraulic fluid supplied from the pump toward the motor so that, in a low engine revolution speed range, the ratio of the partial relief is decreased as the engine temperature increases, but in a high engine revolution speed range, the ratio of the partial relief is increased as the engine revolution speed increases.