Chinese Grammar Error Correction (CGEC) aims to identify and correct grammatical errors in Chinese sentences. Fine-tuning Large Language Models (LLMs) is a popular current method. However, we have observed a significant flaw: LLMs learn grammatical knowledge but often fail to explicitly use specific grammatical concepts to correct erroneous sentences, leading to multiple corrections without a clear indication of which is the most reliable. Humans possess an "intuitive thinking" mode, which allows them to quickly decide which correction is more reliable based on experience and intuition. To address this deficiency in LLMs, we propose the Expanding Intuitive Thinking Model (ExIT). ExIT extends the thinking process of LLMs for CGEC, providing them with a human-like rapid decision-making process. This enables LLMs to quickly select a more reliable correction from multiple alternatives based on experience and intuition. Unlike the LLM decoding process, which focuses only on the trustworthiness of local tokens, this is a global thinking process concerning the erroneous sentence and its correction. ExIT is a lightweight model that performs rapid computations without significantly increasing overhead. Our experimental results on CGEC datasets demonstrate that the proposed ExIT can substantially unleash the error correction potential of LLMs.