Spelling errors in Chinese idioms frequently occur due to various types of misspellings and optical character recognition (OCR) errors in daily learning and usage. Achieving automatic error correction for Chinese idioms is one of the important natural language processing tasks, as it helps improve the quality of Chinese texts as well as language learning. Existing methods, such as edit distance and custom dictionary approaches, suffer from limited error correction capability, low computational efficiency, and weak flexibility. To address these limitations, this paper proposes a novel automatic error correction method for Chinese idioms based on the hidden Markov model (HMM). Specifically, the generation process of idiom spelling errors is modeled using an HMM, transforming the idiom correction problem into a matching task between erroneous idioms and legitimate idioms. By constructing a legitimate idiom table and a Chinese character confusion set, a prototype system for idiom correction was developed, and performance testing was completed. Experiment results demonstrate that the proposed model is simpler with fewer parameters and has lower computational complexity while exhibiting stronger error correction capability and parameter robustness as compared to existing methods. It can more flexibly correct diverse types of idiom errors, showing high potential application value.