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Despite the success achieved in neural abstractive summarization based on pre-trained language models, one unresolved issue is that the generated summaries are not always faithful to the input document. There are two possible causes of the unfaithfulness problem: (1) the summarization model fails to understand or capture the gist of the input text, and (2) the model over-relies on the language model to generate fluent but inadequate words. In this work, we propose a Faithfulness Enhanced Summarization model (FES), which is designed for addressing these two problems and improving faithfulness in abstractive summarization. For the first problem, we propose to use question-answering (QA) to examine whether the encoder fully grasps the input document and can answer the questions on the key information in the input. The QA attention on the proper input words can also be used to stipulate how the decoder should attend to the source. For the second problem, we introduce a max-margin loss defined on the difference between the language and the summarization model, aiming to prevent the overconfidence of the language model. Extensive experiments on two benchmark summarization datasets, CNN/DM and XSum, demonstrate that our model significantly outperforms strong baselines. The evaluation of factual consistency also shows that our model generates more faithful summaries than baselines.