Chinese short text matching usually employs word sequences rather than character sequences to get better performance. However, Chinese word segmentation can be erroneous, ambiguous or inconsistent, which consequently hurts the final matching performance. To address this problem, we propose neural graph matching networks, a novel sentence matching framework capable of dealing with multi-granular input information. Instead of a character sequence or a single word sequence, paired word lattices formed from multiple word segmentation hypotheses are used as input and the model learns a graph representation according to an attentive graph matching mechanism. Experiments on two Chinese datasets show that our models outperform the state-of-the-art short text matching models.