The biometric authentication system is demanded to identify a particular person from the set of persons. Even though many biometric authentication methods are available such as fingerprint, palm, face, and iris, the iris-based recognition system is effective due to its simplified process. This article proposes an iris recognition system using a hybrid classification approach for security applications. The proposed method includes three modules: preprocessing, augmentation, and classifier. The preprocessing module converts the color iris images into grey scale images and also resizes the image into 256 × 256. The preprocessed iris images are now data augmented to construct the larger dataset. The data augmented images are classified into either genuine or imposter images using a hybrid classification approach. The hybrid classification approach functions in two modes as training and testing. In this article, the Convolutional Neural Networks (CNN) is integrated with the Adaptive Neuro-Fuzzy Inference System (ANFIS) classifier to enhance the recognition rate of the iris recognition system. The performance analysis of the proposed approach is shown in terms of sensitivity, accuracy, recognition rate, specificity, false-positive rate, and false-negative rate. The experimental results of the proposed iris recognition system stated in this article significantly outweigh other design methods.