Conventional intra prediction usually utilizes the top and left reconstructed reference samples of the current block to generate prediction pixels. However, with the distance between reference samples and the predicting pixel increasing, the correlation of them becomes weaker. The loss of the bottom-right corner of the current block is bigger than that of the top-left corner. To improve the situation above mentioned, a novel secondary intra prediction scheme is proposed for video coding in this paper. In this scheme, the block will be predicted twice and the first prediction is the same as the conventional intra prediction. After the first prediction, the boundary samples of the reconstructed block can be applied as the reference samples for the second prediction. In our second prediction, the current block is predicted with a designed distance-based bi-directional prediction method. The optimal prediction is determined through the rate-distortion optimization (RDO) strategy. Experimental results show that the proposed algorithm achieves about 3.4% bitrate savings on average comparing to HEVC reference software HM16.9.