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In mobile communications, plenty of textual messages need to be transmitted and processed rapidly. However, messages usually contain noise, which will affect the performance of related applications. Thus, we investigate grammatical error correction (GEC) to correct errors in messages. Unlike recent works, we focus on improving the efficiency of GEC because low time delay is significant in mobile communications. We propose a novel multi-task learning approach to GEC by detecting errors first and then making corrections. Two classifiers are used to serially detect sentence-level and token-level errors, so the correct content can be free from correction operations. We adapt a non-autoregressive decoder to parallelly generate corrected tokens, making the correction stage efficient. Experiments show that our approach is ten times faster than the traditional approach and can achieve a comparable GEC performance. [ABSTRACT FROM AUTHOR]