Abstract Grammatical error correction (GEC) is the task of detecting and correcting grammatical errors in texts written by second language learners. The statistical machine translation (SMT) approach to GEC, in which sentences written by second language learners are translated to grammatically correct sentences, has achieved state-of-the-art accuracy. However, the SMT approach is unable to utilize global context. In this paper, we propose a novel approach to improve the accuracy of GEC, by exploiting the n-best hypotheses generated by an SMT approach. Specifically, we build a classifier to score the edits in the n-best hypotheses. The classifier can be used to select appropriate edits or re-rank the n-best hypotheses. We apply these methods to a state-of-the-art GEC system that uses the SMT approach. Our experiments show that our methods achieve statistically significant improvements in accuracy over the best published results on a benchmark test dataset on GEC.