A linear transform based motion compensated prediction (LT-MCP) scheme is proposed in this paper to improve the efficiency of inter-frame prediction when the intensity of luminance changes abruptly across frames. Either uniform or non-uniform intensity changes can be well processed as the proposed scheme is applied at macroblock (MB) level. LT-MCP is implemented based on the H.264 reference software to evaluate its performance. For those sequences with significant luminance changes across frames, such as Crew, we can achieve about 1.5dB improvement over the conventional MCP with intra prediction disabled and about 0.8dB gain with intra prediction enabled. For those sequences without obvious luminance changes, the proposed scheme also works better.