Recent works in Grammatical Error Correction (GEC) have leveraged the progress in Neural Machine Translation (NMT), to learn rewrites from parallel corpora of grammatically incorrect and corrected sentences, achieving state-of-the-art results. At the same time, Generative Adversarial Networks (GANs) have been successful in generating realistic texts across many different tasks by learning to directly minimize the difference between human-generated and synthetic text. In this work, we present an adversarial learning approach to GEC, using the generator-discriminator framework. The generator is a Transformer model, trained to produce grammatically correct sentences given grammatically incorrect ones. The discriminator is a sentence-pair classification model, trained to judge a given pair of grammatically incorrect-correct sentences on the quality of grammatical correction. We pre-train both the discriminator and the generator on parallel texts and then fine-tune them further using a policy gradient method that assigns high rewards to sentences which could be true corrections of the grammatically incorrect text. Experimental results on FCE, CoNLL-14, and BEA-19 datasets show that Adversarial-GEC can achieve competitive GEC quality compared to NMT-based baselines.