This paper describes a fast block matching algorithm (BMA) for motion estimation exploiting the center-biased motion vector distribution characteristic more efficiently than center-biased hybrid search(CBHS)[1] algorithm. This proposed algorithm, which is called the fast center-biased hybrid search (FCBHS), employ a hybrid method of a compact plus shaped search and a X-shaped search and a diamond search to reduce the search point for motion vectors which distributed within 2pels radius of center of search window. Experimental result show that the FCBHS algorithm is about 44 times faster than Full Search and 7~10% faster than CBHS algorithm. Such as our fast suboptimal motion estimation algorithm is essential for which having limited processing power and constrained on the amount of power-consumption likely real-time mobile video coding applications. This paper compares the popular suboptimal block-matching technique with FCBHS in which both the processing speed and accuracy of motion compensation are tested over widely used H.263 test video sequences.