Natural language inference aims to predict whether a premise sentence can infer another hypothesis sentence. Recent progress on this task only relies on a shallow interaction between sentence pairs, which is insufficient for modeling complex relations. In this paper, we present an attention-fused deep matching network (AF-DMN) for natural language inference. Unlike existing models, AF-DMN takes two sentences as input and iteratively learns the attention-aware representations for each side by multi-level interactions. Moreover, we add a self-attention mechanism to fully exploit local context information within each sentence. Experiment results show that AF-DMN achieves state-of-the-art performance and outperforms strong baselines on Stanford natural language inference (SNLI), multi-genre natural language inference (MultiNLI), and Quora duplicate questions datasets.