Adversarial training (AT) as a regularization method has proved its effectiveness on various tasks. Though there are successful applications of AT on some NLP tasks, the distinguishing characteristics of NLP tasks have not been exploited. In this paper, we aim to apply AT on machine reading comprehension (MRC) tasks. Furthermore, we adapt AT for MRC tasks by proposing a novel adversarial training method called PQAT that perturbs the embedding matrix instead of word vectors. To differentiate the roles of passages and questions, PQAT uses additional virtual P/Q-embedding matrices to gather the global perturbations of words from passages and questions separately. We test the method on a wide range of MRC tasks, including span-based extractive RC and multiple-choice RC. The results show that adversarial training is effective universally, and PQAT further improves the performance.