Recognizing implicit discourse relations is a challenging but important task in the field of Natural Language Processing. For such a complex text processing task, different from previous studies, we argue that it is necessary to repeatedly read the arguments and dynamically exploit the efficient features useful for recognizing discourse relations. To mimic the repeated reading strategy, we propose the neural networks with multi-level attention (NNMA), combining the attention mechanism and external memories to gradually fix the attention on some specific words helpful to judging the discourse relations. Experiments on the PDTB dataset show that our proposed method achieves the state-of-art results. The visualization of the attention weights also illustrates the progress that our model observes the arguments on each level and progressively locates the important words.