In this paper, we focus on the robustness evaluation of Chinese Question Matching (QM) models. Most of the previous work on analyzing robustness issues focus on just one or a few types of artificial adversarial examples. Instead, we argue that a comprehensive evaluation should be conducted on natural texts, which takes into account the fine-grained linguistic capabilities of QM models. For this purpose, we create a Chinese dataset namely DuQM which contains natural questions with linguistic perturbations to evaluate the robustness of QM models. DuQM contains 3 categories and 13 subcategories with 32 linguistic perturbations. The extensive experiments demonstrate that DuQM has a better ability to distinguish different models. Importantly, the detailed breakdown of evaluation by the linguistic phenomena in DuQM helps us easily diagnose the strength and weakness of different models. Additionally, our experiment results show that the effect of artificial adversarial examples does not work on natural texts. Our baseline codes and a leaderboard are now publicly available.