Identifying multiple emotions in a sentence is an important research topic. Existing methods usually model the problem as multi-label classification task. However, previous methods have two issues, limiting the performance of the task. First, these models do not consider prior emotion distribution in a sentence. Second, they fail to effectively capture the context information closely related to the corresponding emotion. In this paper, we propose a Latent Emotion Memory network (LEM) for multi-label emotion classification. The proposed model can learn the latent emotion distribution without external knowledge, and can effectively leverage it into the classification network. Experimental results on two benchmark datasets show that the proposed model outperforms strong baselines, achieving the state-of-the-art performance.