OBJECTIVE: Obstructive sleep apnea (OSA) is a respiratory disease associated with autonomic nervous system dysfunction. As a novel method for analyzing OSA depending on heart rate variability, fuzzy approximate entropy of extrema based on multiple moving averages (Emma-fApEn) can effectively assess the sympathetic tension limits, thereby realizing a good performance in the disease severity screening. METHOD: Sixty 6-h electrocardiogram recordings (20 healthy, 16 mild/moderate OSA and 34 severe OSA) from the PhysioNet database were used in this study. The performances of minima of Emma-fApEn (fApEn-minima), maxima of Emma-fApEn (fApEn-maxima) and classic time-frequency domain indices for each recording were assessed by significance analysis, correlation analysis, parameter optimization and OSA screening. RESULTS: fApEn-minima and fApEn-maxima had significant differences between the severe OSA group and the other two groups, while the mean value (Mean) and the ratio of low-frequency power and high-frequency power (LH) could significantly differentiate OSA recordings from healthy recordings. The correlation coefficient between fApEn-minima and apnea-hypopnea index was the highest (|R| = 0.705). Machine learning methods were used to evaluate the performances of the above four indices. Random forest (RF) achieved the highest accuracy of 96.67% in OSA screening and 91.67% in severe OSA screening, with a good balance in both. CONCLUSION: Emma-fApEn may be used as a simple preliminary detection tool to assess the severity of OSA prior to polysomnography analysis.