An outdoor fan motor driving device and an air conditioner including an outdoor fan motor driving device are provided, which may include an inverter to convert DC power into AC power according to a switching operation and to output the converted AC power to an outdoor fan motor, an output current detector to detect phase currents flowing in the outdoor fan motor, and a controller to control the inverter based on the detected phase currents. When the outdoor fan motor is rotated by external wind, in a state in which all of lower arm switching elements, among upper arm switching elements and lower arm switching elements of the inverter, are turned on before the outdoor fan motor is driven, with the result that levels of the phase currents flowing in the outdoor fan motor are between a first level and a second level, the controller may control the outdoor fan motor such that a rotational speed of the outdoor fan motor is increased while the outdoor fan motor is rotated in a first direction and then rotated in a second direction opposite to the first direction during a speed increase period of the outdoor fan motor after an alignment period during which a rotor of the outdoor fan motor is aligned when the outdoor fan motor is driven.