A sequence-to-sequence (seq2seq) learning with neural networks empirically shows to be an effective framework for grammatical error correction (GEC), which takes a sentence with errors as input and outputs the corrected one. However, the performance of GEC models with the seq2seq framework heavily relies on the size and quality of the corpus on hand. We propose a method inspired by adversarial training to generate more meaningful and valuable training examples by continually identifying the weak spots of a model, and to enhance the model by gradually adding the generated adversarial examples to the training set. Extensive experimental results show that such adversarial training can improve both the generalization and robustness of GEC models.