In modern society, iris recognition has become increasingly popular. The security risk of iris recognition is increasing rapidly because of the attack by various patterns of fake iris. A German hacker organization called Chaos Computer Club cracked the iris recognition system of Samsung Galaxy S8 recently. In view of these risks, iris liveness detection has shown its significant importance to iris recognition systems. The state-of-the-art algorithms mainly rely on hand-crafted texture features which can only identify fake iris images with single pattern. In this paper, we proposed a Hierarchical Multi-class Iris Classification (HMC) for liveness detection based on CNN. HMC mainly focuses on iris liveness detection of multi-pattern fake iris. The proposed method learns the features of different fake iris patterns by CNN and classifies the genuine or fake iris images by hierarchical multi-class classification. This classification takes various characteristics of different fake iris patterns into account. All kinds of fake iris patterns are divided into two categories by their fake areas. The process is designed as two steps to identify two categories of fake iris images respectively. Experimental results demonstrate an extremely higher accuracy of iris liveness detection than other state-of-the-art algorithms. The proposed HMC remarkably achieves the best results with nearly 100% accuracy on ND-Contact, CASIA-Iris-Interval, CASIA-Iris-Syn and LivDet-Iris-2017-Warsaw datasets. The method also achieves the best results with 100% accuracy on a hybrid dataset which consists of ND-Contact and LivDet-Iris-2017-Warsaw datasets.