The latest video coding standard High Efficiency Video Coding (HEVC) can achieve much higher coding efficiency than previous video coding standards. Particularly, by exploiting the hierarchical B-picture prediction structure, temporal redundancy among neighbor frames is eliminated remarkably well. In practice, videos available to consumers usually contain many repeated shots, such as TV series, movies, and talk shows. According to our observations, when these videos are encoded by HEVC with the hierarchical B-picture structure, the temporal correlation in each shot is well exploited. However, the long-term correlation between repeated shots has not been used. We propose a long-term prediction (LTP) scheme to use the long-term temporal correlation between correlated shots in a video. The long-term reference (LTR) frames of a source video are chosen by clustering similar shots and extracting the representative frames, and a modified hierarchical B-picture coding structure based on an LTR frame is introduced to support long-term temporal prediction. An adaptive quantization method is further designed for LTR frames to improve the overall video coding efficiency. Experimental results show that up to 22.86% coding gain can be achieved using the new coding scheme.