While large-scale language models (LLMs) have demonstrated remarkable capabilities in specific natural language processing (NLP) tasks, they may still lack proficiency compared to specialized models in certain domains, such as grammatical error correction (GEC). Drawing inspiration from the concept of curriculum learning, we have delved into refining LLMs into proficient GEC experts by devising effective curriculum learning (CL) strategies. In this paper, we introduce a novel approach, termed LLM-based curriculum learning, which capitalizes on the robust semantic comprehension and discriminative prowess inherent in LLMs to gauge the complexity of GEC training data. Unlike traditional curriculum learning techniques, our method closely mirrors human expert-designed curriculums. Leveraging the proposed LLM-based CL method, we sequentially select varying levels of curriculums ranging from easy to hard, and iteratively train and refine using the pretrianed T5 and LLaMA series models. Through rigorous testing and analysis across diverse benchmark assessments in English GEC, including the CoNLL14 test, BEA19 test, and BEA19 development sets, our approach showcases a significant performance boost over baseline models and conventional curriculum learning methodologies.