Intra prediction is an important tool in intra-frame video coding to reduce the spatial redundancy. In current coding standard H.265/high-efficiency video coding (HEVC), a copying-based method based on the boundary (or interpolated boundary) reference pixels is used to predict each pixel in the coding block to remove the spatial redundancy. We find that the conventional copying-based method can be further improved in two cases: 1) the boundary has an inhomogeneous region and 2) the predicted pixel is far away from the boundary that the correlation between the predicted pixel and the reference pixels is relatively weak. This paper performs a theoretical analysis of the optimal weights based on a first-order Gaussian Markov model and the effects when the pixel values deviate from the model and the predicted pixel is far away from the reference pixels. It also proposes a novel intra prediction scheme based on the analysis that smoothing the copying-based prediction can derive a better prediction block. Both the theoretical analysis and the experimental results show the effectiveness of the proposed intra prediction method. An average gain of 2.3% on all intra coding can be achieved with the HEVC reference software.