Text matching is a core natural language processing research problem. How to retain sufficient information on both content and structure information is one important challenge. In this paper, we present a neural approach for general-purpose text matching with deep mutual information estimation incorporated. Our approach, Text matching with Deep Info Max (TIM), is integrated with a procedure of unsupervised learning of representations by maximizing the mutual information between text matching neural network's input and output. We use both global and local mutual information to learn text representations. We evaluate our text matching approach on several tasks including natural language inference, paraphrase identification, and answer selection. Compared to the state-of-the-art approaches, the experiments show that our method integrated with mutual information estimation learns better text representation and achieves better experimental results of text matching tasks without exploiting pretraining on external data.