Many classification models work poorly on short texts due to data sparsity. To address this issue, we propose topic memory networks for short text classification with a novel topic memory mechanism to encode latent topic representations indicative of class labels. Different from most prior work that focuses on extending features with external knowledge or pre-trained topics, our model jointly explores topic inference and text classification with memory networks in an end-to-end manner. Experimental results on four benchmark datasets show that our model outperforms state-of-the-art models on short text classification, meanwhile generates coherent topics.