A printer and a method of driving a cooling fan of the printer include a storage unit temporarily stores printing option data and image data, and a control unit controls an operation of a printing unit in one of a warming-up mode, a standby mode, a printing mode and a sleep mode based on the printing option data and the image data as inputted into the control unit. The control unit outputs a control signal variably controlling an RPM (Rotation Per Minute) of the cooling fan based on the operation mode and a printing speed of the printing unit. A cooling fan driving unit drives the cooling fan at a different RPM based on the control signal input from the control unit. Accordingly, the printer and the method of driving the cooling fan of the printer are capable of shortening the warming-up time to increase an initial printing speed, preventing the printing unit from being overheated, extending a lifespan of the cooling fan, and reducing a power consumption.