A method for controlling speed of a single phase induction motor using frequency variation, including the steps of generating an operation start signal and a speed command signal according to a user's selection, outputting a digital data for formation of a sinusoidal wave signal of a desired frequency, to converting means at an interval of a predetermined time period set by a timer to thereby generate the sinusoidal wave signal of the frequency desired by the user, generating the sinusoidal wave based on the digital data, comparing the sinusoidal wave with a triangular signal for controlling a speed of a motor, and converting a DC voltage from a power source into an AC voltage of a frequency band desired by the user to thereby operate the motor. An apparatus for controlling the speed of a single phase induction motor is also provided.