In this paper, we propose a differential structure of subpixels which are interpolated from integer pixels using ntab linear FIR filters. The generation and management of sub-pixels are a very serious problem in high-definition H.264 video encoding. Since the amount of sub-pixels in H.264 encoding is about 16 times larger than that of integer pixels, H.264 encoder needs very high speed memory access for realtime encoding of high-definition video. In order to avoid the sub-pixel problem, we estimate the distortion value for a motion estimation of sub-pixel resolution by using the nonlinear combination of the distortion value derived from a motion estimation of related integer pixel, based on the proposed differential structure. Simulation results show that the proposed mathematical properties are valid by the sub-pixel motion estimation based on the proposed mathematical analysis. It also shows that the proposed sub-pixel motion estimation is so effective that the encoding speed is dramatically increased without a considerable depression of video quality.