Provided are a method and apparatus for compensating motion of a moving image. The method includes calculating a pixel value of a pixel located between pixels of a reference image corresponding to a current image based on pixel values of the pixels of the reference image by using at least one method from among a plurality of methods, such as a vertical linear filtering, a horizontal linear filtering, and a cubic filtering, of interpolating the pixels of the reference image according to codec information indicating one of a plurality of codecs, such as MPEG4, H.264/AVC, and VC1, and restoring the current image by adding motion compensation data, including the calculated pixel value, and a difference between the reference image and the current image.