In this article the new hybrid iris image segmentation method based on convolutional neural networks and mathematical methods is proposed. Iris boundaries are found using modified Daugman’s method. Two UNet-based convolutional neural networks are used for iris mask detection. The first one is used to predict the preliminary iris mask including the areas of the pupil, eyelids and some eyelashes. The second neural network is applied to the enlarged image to specify thin ends of eyelashes. Then the principal curvatures method is used to combine the predicted by neural networks masks and to detect eyelashes correctly. The pro- posed segmentation algorithm is tested using images from CASIA IrisV4 Interval database. The results of the proposed method are evaluated by the Intersection over Union, Recall and Precision metrics. The average metrics values are 0.922, 0.957 and 0.962, respectively. The proposed hy- brid iris image segmentation approach demonstrates an improvement in comparison with the methods that use only neural networks.