Motion estimation can effectively remove the time-domain redundancy in adjacent frames and greatly reduce the bit rate, so it is widely used in video coding and decoding standards. Motion estimation is also the most computationally intensive and time-consuming module in video coding, so the research on fast motion estimation algorithm has been a hot topic in the field of video coding. In this paper, an innovative parallel fast sub-pixel motion estimation algorithm is proposed for sub-pixel prediction in motion estimation. The algorithm obtains the optimal integer pixel prediction point and 8 adjacent integer pixel points by the integer pixel motion estimation, and uses the 5-parameter quadratic function to fit the residual surface function, and the half-pixel point with the smallest value of the surface function is taken as the optimal 1/2 pixel point. The optimal 1/2 pixel point and an integer pixel at a specific position are taken to infer a suboptimal 1/2 pixel point, and finally search for 12 1/4 pixel points around the optimal 1/2 pixel and sub-optimal 1/2 pixel to determine the optimal 1/4 pixel. Experimental result shows that, under the condition that the image coding quality is basically unchanged, the algorithm can significantly reduce the number of sub-pixel searched points, and effectively reduce the sub-pixel prediction time and computational complexity.