Virtual Reality 360 degree video is spherical video. It allows the viewer to freely choose the field of view from any angle, and the video resolution must be high enough for every field of view. During coding process, spherical video is projected into 2D plane video and it has ultra-high resolution and larger data compared to traditional video. Considering reducing the high spatial redundancy of virtual reality 360 degree video, and reducing the computational complexity of intra coding, while ensuring the integrity of the details of each field of view, a fast intra prediction algorithm for virtual reality 360 degree video based on improved Rough Mode Decision (RMD) is proposed. The experimental results show that the proposed algorithm brings 38.73% time saving with only 1.4% Bjontegaard delta rate increase in All-Intra mode.