There is provided an image encode apparatus which comprises a generation means for generating a prediction error from an encode target pixel value and a prediction value of the encode target pixel value, a judgment means for generating a generation frequency distribution of the prediction error to judge whether or not the generation frequency distribution is discrete and an entropy encode means for changing encode data corresponding to the prediction error and performing entropy encoding on the obtained encode data, in accordance with a judged result by the judgment means. Therefore, the encoding can be effectively performed even on such the image data having the discrete pixel value as in a CG image, a limited-color image or the like.