In this study, we explore cross-lingual transfer learning in grammatical error correction (GEC) tasks. Many languages lack the resources required to train GEC models. Cross-lingual transfer learning from high-resource languages (the source models) is effective for training models of low-resource languages (the target models) for various tasks. However, in GEC tasks, the possibility of transferring grammatical knowledge (e.g., grammatical functions) across languages is not evident. Therefore, we investigate cross-lingual transfer learning methods for GEC. Our results demonstrate that transfer learning from other languages can improve the accuracy of GEC. We also demonstrate that proximity to source languages has a significant impact on the accuracy of correcting certain types of errors.