Obstructive sleep apnea (OSA) is a common sleep disorder that is often associated with reduced heart rate variability (HRV), thus reflecting modulation of the autonomic system. Sliding trend fuzzy approximate entropy (SlTr-fApEn), which is based on the empirical mode decomposition (EMD) method, has been proposed as a novel index for analyzing HRV with OSA. This study included 60 electrocardiogram recordings from the PhysioNet database (40 OSA recordings and 20 healthy recordings) with apnea or no apnea in 5-minute segments. HRV indices obtained by sliding trend analysis were compared to those obtained by time-frequency domain analysis. Among all indices, the ratio of low-frequency power and high-frequency power (LF/HF) and sliding trend indices could significantly differentiate OSA recordings from normal recordings (p < 0.05). The OSA screening accuracy of SlTr-fApEn (85%) was higher than that of LF/HF (80%). Disease state analysis showed significant differences in SlTr-fApEn among the control group, normal OSA group, and apnea OSA group (p < 0.05). Therefore, SlTr-fApEn can reflect the complexity of autonomic changes during a short time period.