Iris recognition has been used as one of the biometric systems for user authentication, identification, and verification for quite some time. The basis of an iris recognition lies on the matching algorithm, which requires similarities of the iris data in the database with the captured one. In addition, nowadays using non-cosmetic or prescribed contact lenses becomes more popular and more preferred choice of many people, which makes the number of contact lens wearers significantly increases. These eyes with contact lenses add more complexity to the iris recognition process, since it can disturb the matching process which then affect the performance of the system. This situation has motivated this study to propose an iris recognition system that works for eyes with lenses. The proposed iris recognition system for eyes wearing non-cosmetic contact lenses was developed using circular hough transform (CHT) in the preprocessing phase for iris localization and discrete wavelet transform (DWT) for feature extraction. Experiments conducted on the proposed system has shown promising results with good accuracy of 0.95 for eyes with no contact lens and 0.8 for eyes with non-cosmetic lenses. The findings also suggested the importance of the iris localization process to the performance of the recognition system.