Abstract Background Accurately prioritizing candidate disease genes is an important and challenging problem. Various network-based methods have been developed to predict potential disease genes by utilizing the disease similarity network and molecular networks such as protein interaction or gene co-expression networks. Although successful, a common limitation of the existing methods is that they assume all diseases share the same molecular network and a single generic molecular network is used to predict candidate genes for all diseases. However, different diseases tend to manifest in different tissues, and the molecular networks in different tissues are usually different. An ideal method should be able to incorporate tissue-specific molecular networks for different diseases. Results In this paper, we develop a robust and flexible method to integrate tissue-specific molecular networks for disease gene prioritization. Our method allows each disease to have its own tissue-specific network(s). We formulate the problem of candidate gene prioritization as an optimization problem based on network propagation. When there are multiple tissue-specific networks available for a disease, our method can automatically infer the relative importance of each tissue-specific network. Thus it is robust to the noisy and incomplete network data. To solve the optimization problem, we develop fast algorithms which have linear time complexities in the number of nodes in the molecular networks. We also provide rigorous theoretical foundations for our algorithms in terms of their optimality and convergence properties. Extensive experimental results show that our method can significantly improve the accuracy of candidate gene prioritization compared with the state-of-the-art methods. Conclusions In our experiments, we compare our methods with 7 popular network-based disease gene prioritization algorithms on diseases from Online Mendelian Inheritance in Man (OMIM) database. The experimental results demonstrate that our methods recover true associations more accurately than other methods in terms of AUC values, and the performance differences are significant (with paired t-test p-values less than 0.05). This validates the importance to integrate tissue-specific molecular networks for studying disease gene prioritization and show the superiority of our network models and ranking algorithms toward this purpose. The source code and datasets are available at http://nijingchao.github.io/CRstar/ .