Context modeling has a pivotal role in open domain conversation. Existing works either use heuristic methods or jointly learn context modeling and response generation with an encoder-decoder framework. This paper proposes an explicit context rewriting method, which rewrites the last utterance by considering context history. We leverage pseudo-parallel data and elaborate a context rewriting network, which is built upon the CopyNet with the reinforcement learning method. The rewritten utterance is beneficial to candidate retrieval, explainable context modeling, as well as enabling to employ a single-turn framework to the multi-turn scenario. The empirical results show that our model outperforms baselines in terms of the rewriting quality, the multi-turn response generation, and the end-to-end retrieval-based chatbots.