Dense passage retrieval has been shown to be an effective approach for information retrieval tasks such as open domain question answering. Under this paradigm, a dual-encoder model is learned to encode questions and passages separately into vector representations, and all the passage vectors are then pre-computed and indexed, which can be efficiently retrieved by vector space search during inference time. In this paper, we propose a new contrastive learning method called Cross Momentum Contrastive learning (xMoCo), for learning a dual-encoder model for question-passage matching. Our method efficiently maintains a large pool of negative samples like the original MoCo, and by jointly optimizing question-to-passage and passage-to-question matching tasks, enables using separate encoders for questions and passages. We evaluate our method on various open-domain question answering dataset, and the experimental results show the effectiveness of the proposed method.