Modeling cyber risks has been an important but challenging task in the domain of cyber security. It is mainly because of the high dimensionality and heavy tails of risk patterns. Those obstacles have hindered the development of statistical modeling of the multivariate cyber risks. In this work, we propose a novel approach for modeling the multivariate cyber risks which relies on the deep learning and extreme value theory. The proposed model not only enjoys the high accurate point predictions via deep learning but also can provide the satisfactory high quantile prediction via extreme value theory. The simulation study shows that the proposed model can model the multivariate cyber risks very well and provide satisfactory prediction performances. The empirical evidence based on real honeypot attack data also shows that the proposed model has very satisfactory prediction performances.