The iris is one of the most secure biometric types of information that is widely employed in authentication systems. In this paper we present a method for iris recognition based on the Contourlet Transform and Shannon Entropy which entails (i) the detection and segmentation of the iris, (ii) its normalization, (iii) the application of the Contourlet Transform, (iv) the generation of the iris descriptor, and (v) the matching between the query iris and those in the database. The proposed method has been tested with images taken from the popular CASIA-V4 and UBIRIS.v1 datasets and compared against other six recent iris recognition algorithms using the statistics EER, AUC and ARR. The results show a higher performance of the proposed method with a reduced computation time.