Intra prediction is a very important tool in current video coding standards. High-efficiency video coding (HEVC) intra prediction presents relevant gains in encoding efficiency when compared to previous standards, but with a very important increase in the computational complexity since 33 directional angular modes must be evaluated. Motivated by this high complexity, this article presents a complexity reduction algorithm developed to reduce the HEVC intra mode decision complexity targeting multiview videos. The proposed algorithm presents an efficient fast intra prediction compliant with singleview and multiview video encoding. This fast solution defines a reduced subset of intra directions according to the video texture and it exploits the relationship between prediction units (PUs) of neighbor depth levels of the coding tree. This fast intra coding procedure is used to develop an inter-view prediction method, which exploits the relationship between the intra mode directions of adjacent views to further accelerate the intra prediction process in multiview video encoding applications. When compared to HEVC simulcast, our method achieves a complexity reduction of up to 47.77%, at the cost of an average BD-PSNR loss of 0.08 dB.