Document Visual Question Answering (VQA) aims to answer questions over visually-rich documents. In this work, we introduce a new Document VQA dataset, named TAT-DQA, which consists of 3,067 document pages comprising semi-structured table(s) and unstructured text as well as 16,558 question-answer pairs. The documents are sampled from financial reports and contain lots of numbers, which means discrete reasoning capability is demanded to answer the questions. Based on TAT-DQA, we further develop a novel model named MHST that takes into account the information in multi-modalities to intelligently address different types of questions with corresponding strategies, i.e., extraction or reasoning. The experiments show that MHST model significantly outperforms the baseline methods, demonstrating its effectiveness. However, the performance still lags far behind that of human experts. We expect that our TAT-DQA dataset would facilitate the research on understanding of visually-rich documents, especially for scenarios that require discrete reasoning. Also, we hope the proposed model would inspire researchers to design more advanced Document VQA models in future.