English grammar error correction, as a subtask in the field of natural language processing, can provide second language learners with services such as automatic correction of grammatical errors and article touch-up. Based on the current mainstream neural machine grammar error correction methods, this paper proposes an English grammar error correction model based on the Transformer model incorporating the replication mechanism (C-Transformer). Combining this model with the pinyin detection algorithm and the feedback filtering algorithm, and expanding the training data by creating pseudo-parallel sentence pairs, an automatic English grammar error correction system is successfully designed. Compared with the traditional CAMB grammar error correction model, the accuracy, recall and F0.5 metrics of this paper’s model are improved by 16.68%, 20.38% and 17.33%, respectively. Moreover, in the English composition correction experiments for Chinese students, the average precision rate, recall rate and F1 value of this paper’s model for various types of grammatical error correction reached 84.70%, 71.85% and 77.75%, respectively, proving the effectiveness and superiority of this paper’s model. In addition, using the designed English grammar automatic error correction system to conduct teaching experiments, students’ knowledge of various grammar questions, especially in writing, was significantly improved, indicating that the designed system has a better application effect, which is of great significance for improving the effectiveness of university English teaching.