The traditional English grammar error correction system has problems such as poor error recognition precision and error correction success rate to be improved. Therefore, in this study, data augmentation techniques were used to transform and process error correcting English texts, and a rule-based and shallow neural network-based English text grammar correction model was constructed. The experimental results showed that the grammar error generation (GEG), rule-based (RB), classification-based (CB), and recurrent neural network (RNN) models achieved accuracy rates of 93.92%, 82.17%, 79.41%, and 88.09% in correcting grammar errors on 1702641 test sentences in the One Billion word corpus, respectively. The experimental results showed that the English grammar error correction model designed in this study had a strong error correction ability, but the computational efficiency was low. The research results significantly improved the accuracy and generalization ability of English grammar correction, optimized learning costs, and brought positive impacts to educational applications, providing strong support for the development of intelligent English grammar correction.