An apparatus and method for processing a video signal, and particularly, an apparatus and method for deleting a sawtooth wave are provided in which a sawtooth wave component is detected and with consideration of direction the sawtooth wave is deleted. The sawtooth wave deleting method includes (a) detecting a sawtooth wave component based on an area dispersion value and motion information in each frame in an input video signal; (b) detecting a direction from the pixels of the detected sawtooth wave component; and (c) deleting the sawtooth wave component by outputting an interpolated pixel in the detected direction. According to the apparatus and method, since interpolation of a sawtooth wave component is performed with consideration of the direction so that the sawtooth wave component is effectively deleted, a much smoother image is provided after deinterlacing.