1. A method of encoding an image by using motion prediction, the method comprising: determining weights for respective low-precision sub-pixels for interpolation between the low-precision sub-pixels to determine a high-precision sub-pixel between the low-precision sub-pixels; determining an interpolation direction for the low-precision sub-pixels based on a position of the high-precision sub-pixel; performing motion prediction in units of high-precision sub-pixels determined by interpolation which applies the interpolation direction and the weights to the low-precision sub-pixels; and encoding information about a weight for interpolation for the high-precision sub-pixel and a motion vector for a predetermined-precision sub-pixel, as motion prediction information for the high-precision sub-pixel, wherein the predetermined precision is equal to or higher than precisions of the low-precision sub-pixels and is lower than a precision of the high-precision sub-pixel.