Yes / Multimodal biometric systems have been widely applied in many real-world applications due to its ability to deal with a number of significant limitations of unimodal biometric systems, including sensitivity to noise, population coverage, intra-class variability, non-universality, and vulnerability to spoofing. In this paper, an efficient and real-time multimodal biometric system is proposed based on building deep learning representations for images of both the right and left irises of a person, and fusing the results obtained using a ranking-level fusion method. The trained deep learning system proposed is called IrisConvNet whose architecture is based on a combination of Convolutional Neural Network (CNN) and Softmax classifier to extract discriminative features from the input image without any domain knowledge where the input image represents the localized iris region and then classify it into one of N classes. In this work, a discriminative CNN training scheme based on a combination of back-propagation algorithm and mini-batch AdaGrad optimization method is proposed for weights updating and learning rate adaptation, respectively. In addition, other training strategies (e.g., dropout method, data augmentation) are also proposed in order to evaluate different CNN architectures. The performance of the proposed system is tested on three public datasets collected under different conditions: SDUMLA-HMT, CASIA-Iris- V3 Interval and IITD iris databases. The results obtained from the proposed system outperform other state-of-the-art of approaches (e.g., Wavelet transform, Scattering transform, Local Binary Pattern and PCA) by achieving a Rank-1 identification rate of 100% on all the employed databases and a recognition time less than one second per person.