OBJECTIVE: The purpose of this study was to evaluate whether the complexity of the corneal pulse (CP) signal can be used to differentiate patients with primary open-angle glaucoma (POAG) from healthy subjects. APPROACH: The study sample consisted of 28 patients with POAG and a control, age-matched group of 30 subjects. After standard ophthalmic examination, the CP signal from a randomly selected eye of each participant was measured using non-contact ultrasonic micro-displacement measurement technology. After pre-processing, the complexity of the CP signal was estimated using refined composite multiscale fuzzy entropy (RCMFE) up to scale factor 50. The average RCMFE values were computed from three repeated measurements of the CP signals for each participant and each scale factor. MAIN RESULTS: The complexity of the CP signal in glaucomatous eyes was higher than that observed in healthy ones. Also, RCMFE of the CP signal was found to differentiate (statistically significantly) between the two groups for scales in the range from 26 to 43. For these scales, the one for which the lowest p-value (t-test, p = 0.017) was obtained when comparing RCMFE between the two groups was selected as the optimal scale. Next, a receiver operating characteristic analysis for the optimal scale showed that the proposed approach of calculating the multiscale entropy of the CP signal has some potential to discriminate between patients with POAG and healthy controls (sensitivity, specificity and accuracy of 0.643, 0.700 and 0.672, respectively). SIGNIFICANCE: In conclusion, RCMFE, as a complexity measure, may be considered an auxiliary indicator to support glaucoma diagnostics.