Grammatical Error Correction (GEC) is the task of correcting errorful sentences into grammatically correct, semantically consistent, and coherent sentences. Popular GEC models either use large-scale synthetic corpora or use a large number of human-designed rules. The former is costly to train, while the latter requires quite a lot of human expertise. In recent years, AMR, a semantic representation framework, has been widely used by many natural language tasks due to its completeness and flexibility. A non-negligible concern is that AMRs of grammatically incorrect sentences may not be exactly reliable. In this paper, we propose the AMR-GEC, a seq-to-seq model that incorporates denoised AMR as additional knowledge. Specifically, We design a semantic aggregated GEC model and explore denoising methods to get AMRs more reliable. Experiments on the BEA-2019 shared task and the CoNLL-2014 shared task have shown that AMR-GEC performs comparably to a set of strong baselines with a large number of synthetic data. Compared with the T5 model with synthetic data, AMR-GEC can reduce the training time by 32% while inference time is comparable. To the best of our knowledge, we are the first to incorporate AMR for grammatical error correction.