An apparatus and method for driving a motor of an air conditioner are disclosed. A method for driving a motor of an air conditioner includes driving the motor in response to a predetermined speed command, sequentially detecting first and second mechanical angles in response to the speed command or a reference speed being spaced apart from the speed command by a predetermined range, calculating a maximum speed mechanical angle corresponding to a maximum speed ripple of the motor on the basis of the detected first and second mechanical angles, and compensating for load torque of the motor on the basis of the calculated the maximum speed mechanical angle. As a result, the speed ripple is decreased during the constant speed operation.