Short text matching often faces the challenges that there are great word mismatch and expression diversity between the two texts, which would be further aggravated in languages like Chinese where there is no natural space to segment words explicitly. In this paper, we propose a novel lattice based CNN model (LCNs) to utilize multi-granularity information inherent in the word lattice while maintaining strong ability to deal with the introduced noisy information for matching based question answering in Chinese. We conduct extensive experiments on both document based question answering and knowledge based question answering tasks, and experimental results show that the LCNs models can significantly outperform the state-of-the-art matching models and strong baselines by taking advantages of better ability to distill rich but discriminative information from the word lattice input.