The H.264 standard' describes the intra prediction process to exploit the spatial correlation between adjacent blocks for video compression. The intra prediction for luminance samples can be performed using blocks of size 4x4 or 16x16 pixels. The intra prediction for chrominance samples is performed on 8x8 block size. 4x4 block size luminance samples can be predicted using nine intra prediction modes, 16x16 block size luminance samples and 8x8 block size chrominance samples each can be predicted using four intra prediction modes. The exhaustive evaluation of all possible luminance and chrominance intra prediction modes requires significant amount of computations and thus it reduces the encoding speed. This paper describes a method to approximate optimal luminance intra prediction mode with reduced computations. The results show that significant speed improvement can be gained with negligible loss of objective quality.