A cooling fan driving device including: a hydraulic pump for a cooling fan, the hydraulic pump being driven by an engine; a hydraulic motor to which pressurized oil discharged from the hydraulic pump is supplied and which rotates the cooling fan; an oil temperature sensor which detects temperature of hydraulic oil; a water temperature sensor which detects temperature of refrigerant; a rotational speed sensor which detects the rotational speed of the engine; flow rate control means which controls a flow rate of pressurized oil to be supplied to the hydraulic motor; and a controller which controls the flow rate control means, wherein the controller includes a target rotational speed setting portion which sets the target rotational speed of the cooling fan and a rotational speed command calculation portion which issues a command of the flow rate of pressurized oil supplied to the hydraulic motor, and the target rotational speed setting portion sets the target rotational speed of the cooling fan based on respective detection signals from the oil temperature sensor, the water temperature sensor and the rotational speed sensor, being characterized in that the controller has an acceleration pattern setting portion which sets an acceleration pattern for increasing the rotational speed of the cooling fan to the target rotational speed, the acceleration pattern setting portion sets the acceleration pattern for increasing the rotational speed of the cooling fan to the target rotational speed based on the rotational speed of the engine detected by the rotational speed sensor, the target rotational speed of the cooling fan set at the target rotational speed setting portion, and magnitude of force due to inertia of the cooling fan and the hydraulic motor obtained by a function of motor torque of the hydraulic motor and angular acceleration (dω/dt) of the hydraulic motor, and the rotational speed command calculation portion calculates a command value to control the flow rate control means based on the rotational speed of the engine, the target rotational speed of the cooling fan set at the target rotational speed setting portion, and the acceleration pattern set at the acceleration pattern setting portion so that the rotational speed of the cooling fan is increased from the current rotational speed to the target rotational speed based on the acceleration pattern. a hydraulic pump for a cooling fan, the hydraulic pump being driven by an engine; a hydraulic motor to which pressurized oil discharged from the hydraulic pump is supplied and which rotates the cooling fan; an oil temperature sensor which detects temperature of hydraulic oil; a water temperature sensor which detects temperature of refrigerant; a rotational speed sensor which detects the rotational speed of the engine; flow rate control means which controls a flow rate of pressurized oil to be supplied to the hydraulic motor; and a controller which controls the flow rate control means, wherein the controller includes a target rotational speed setting portion which sets the target rotational speed of the cooling fan and a rotational speed command calculation portion which issues a command of the flow rate of pressurized oil supplied to the hydraulic motor, and the target rotational speed setting portion sets the target rotational speed of the cooling fan based on respective detection signals from the oil temperature sensor, the water temperature sensor and the rotational speed sensor, being characterized in that the controller has an acceleration pattern setting portion which sets an acceleration pattern for increasing the rotational speed of the cooling fan to the target rotational speed, the acceleration pattern setting portion sets the acceleration pattern for increasing the rotational speed of the cooling fan to the target rotational speed based on the rotational speed of the engine detected by the rotational speed sensor, the target rotational speed of the cooling fan set at the target rotational speed setting portion, and magnitude of force due to inertia of the cooling fan and the hydraulic motor obtained by a function of motor torque of the hydraulic motor and angular acceleration (dω/dt) of the hydraulic motor, and the rotational speed command calculation portion calculates a command value to control the flow rate control means based on the rotational speed of the engine, the target rotational speed of the cooling fan set at the target rotational speed setting portion, and the acceleration pattern set at the acceleration pattern setting portion so that the rotational speed of the cooling fan is increased from the current rotational speed to the target rotational speed based on the acceleration pattern.