In this paper, we focus on unsupervised domain adaptation for Machine Reading Comprehension (MRC), where the source domain has a large amount of labeled data, while only unlabeled passages are available in the target domain. To this end, we propose an Adversarial Domain Adaptation framework (AdaMRC), where (i) pseudo questions are first generated for unlabeled passages in the target domain, and then (ii) a domain classifier is incorporated into an MRC model to predict which domain a given passage-question pair comes from. The classifier and the passage-question encoder are jointly trained using adversarial learning to enforce domain-invariant representation learning. Comprehensive evaluations demonstrate that our approach (i) is generalizable to different MRC models and datasets, (ii) can be combined with pre-trained large-scale language models (such as ELMo and BERT), and (iii) can be extended to semi-supervised learning.