Grammatical error correction in English is a long studied problem with many existing systems and datasets. However, there has been only a limited research on error correction of other languages. In this paper, we present a new dataset AKCES-GEC on grammatical error correction for Czech. We then make experiments on Czech, German and Russian and show that when utilizing synthetic parallel corpus, Transformer neural machine translation model can reach new state-of-the-art results on these datasets. AKCES-GEC will be publicly available under CC BY-NC-SA 4.0 license, and the source code of the GEC model will be open sourced.