Motion estimation is a core part of most video compression systems since it directly affects the output video quality and the encoding time. The full search (FS) technique gives the highest visual quality but has the problem of a significant computational load. To solve this problem, we present in this paper a modified median (MMED) operation and advanced search strategies for fast motion estimation. The proposed MMED operation includes a temporally co-located motion vector (MV) to select an appropriate initial candidate. Moreover, we introduce a search procedure that reduces the number of thresholds and simplifies the early termination conditions for the determination of a final MV. The experimental results show that the proposed approach achieves substantial speedup compared with the conventional methods including the motion vector field adaptive search technique (MVFAST) and predictive MVFAST (PMVFAST). The proposed algorithm also improves the PSNR values by increasing the correlation between the MVs, compared with the FS method.