Video compression is the process of reducing the amount of data required to represent digital video while preserving an acceptable video quality. Recent studies on video compression have focused on multimedia transmission, videophones, teleconferencing, high definition television (HDTV), CD-ROM storage, etc. The idea of compression techniques is to remove the redundant information that exists in the video sequences. Motion compensated predictive coding is the main coding tool for removing temporal redundancy of video sequences and it typically accounts for 50-80% of the video encoding complexity. This technique has been adopted by all of the existing international video coding standards. It assumes that the current frame can be locally modelled as a translation of the reference frames. The practical and widely method used to carry out motion compensated prediction is block matching algorithm. In this method, video frames are divided into a set of non-overlapped macroblocks; each target macroblock of the current frame is compared with the search area in the reference frame in order to find the best matching macroblock. This will carry out displacement vectors that stipulate the movement of the macroblocks from one location to another in the reference frame. Checking all these locations is called full Search, which provides the best result. However, this algorithm suffers from long computational time, which necessitates improvement. Several methods of Fast Block Matching algorithm were developed to reduce the computation complexity. This thesis focuses on two classifications: the first is called the lossless block matching algorithm process, in which the computational time required to determine the matching macroblock of the full search is decreased while the resolution of the predicted frames is the same as for the full search. The second is called the lossy block matching algorithm process, which reduces the computational complexity effectively but the search result’s quality is not the same as for the full search.