In video encoding standard, movement estimation has been used to minimize redundancy between close scenes. The video compressing standard H.264 which is most generally used in current, and the following standard HEVC use sub-pixel motion estimation for the accuracy of estimation so that they could improve the performance of video encoding even higher than the former video coding standard by determining the 1/4 pixel accuracy. Normal video encoding uses motion estimation in spatial domain, which tops the former standard by using motion estimation of 1/4 pixel accuracy, but has problem with the increased computations caused by the application of interpolation technique for expecting the information of sub-pixel. Motion estimation takes 60-80% of the whole encoding time which increases computations, and the computations affect the whole encoding time. The existing half pixel motion estimation that uses shifting matrix in frequency domain could solve the problem with the computation increase caused by interpolation technique in space spatial, but its interpolation performance doesn't deliver high performance because it uses bilinear interpolation. In this paper, i tried to improve the efficiency by applying 3rd function interpolation which is applied motion estimation algorithm using shifting matrix. At the result of experiment, in the case using the suggested method, it has been proved to serve higher performance at PSNR level by having lower computation than the 1/4 pixel motion estimation in spatial domain.