Non-autoregressive (NAR) neural machine translation is usually done via knowledge distillation from an autoregressive (AR) model. Under this framework, we leverage large monolingual corpora to improve the NAR model's performance, with the goal of transferring the AR model's generalization ability while preventing overfitting. On top of a strong NAR baseline, our experimental results on the WMT14 En-De and WMT16 En-Ro news translation tasks confirm that monolingual data augmentation consistently improves the performance of the NAR model to approach the teacher AR model's performance, yields comparable or better results than the best non-iterative NAR methods in the literature and helps reduce overfitting in the training process.