A control method for a fan of a work vehicle includes supplying, when an engine is started, a first current to a solenoid of a variable relief valve such that the hydraulic fluid flows by a first flow rate, supplying, when a rotational speed of the engine becomes larger than a first rotational speed threshold value, a second current larger than the first current to the solenoid such that the hydraulic fluid flows by a second flow rate smaller than the first flow rate to reduce the rotational speed of the fan, and supplying, when the rotational speed of the engine becomes larger than a second rotational speed threshold value that is larger than the first rotational speed threshold value, a current to the solenoid to change the rotational speed of the fan, the current corresponding to a temperature of liquid flowing in the work vehicle.