Intra prediction coding is one of the many coding-efficiency oriented tools of H.264/AVC, but it requires high computational complexity. Many fast intra coding algorithms have been proposed to reduce the computational complexity of intra prediction, but most of them have been focused on the mode decision methods themselves. In this paper, we propose a fast algorithm in which new intra modes are substituted for certain of the conventional intra modes, so that the number of intra modes can be reduced. The proposed intra modes, namely the weighted mean and median modes, can effectively represent the directions of a block in a frame. The simulation results showed that the proposed method could reduce the encoding time of the overall sequence by about 11% and that of the I-frames by about 28%, without any noticeable degradation of the coding efficiency.