The MPEG-4/AVC/H.264 video coding standard adopts various coding schemes such as multiple reference frames and variable block sizes for motion estimation. Hence, MPEG-4/AVC/H.264 provides gains in compression efficiency of up to 50% over a wide range of bit rates and video resolutions compared to previous standards. However, these features result in a considerable increase in encoder complexity, mainly regarding to mode decision and motion estimation. The proposed algorithms use the stored motion vectors to compose the motion vector without performing the full search in each reference frame. Therefore, the proposed algorithms can obtain an average speed up ratio of four for encoding, thus benefiting from the prediction of the motion vector for the reference frames in advance and maintaining good performance. Any fast search algorithm can be utilized to further largely reduce the computational load.