With the rapid development of mobile networks, the people's social contacts have been considerably facilitated. However, the rise of mobile social network fraud upon those networks, has caused a great deal of distress, in case of depleting personal and social wealth, then potentially doing significant economic harm. To detect fraudulent users, call detail record (CDR) data, which portrays the social behavior of users in mobile networks, has been widely utilized. But the imbalance problem in the aforementioned data, which could severely hinder the effectiveness of fraud detectors based on graph neural networks(GNN), has hardly been addressed in previous work. In this paper, we are going to present a novel Cost-Sensitive Graph Neural Network (CSGNN) by creatively combining cost-sensitive learning and graph neural networks. We conduct extensive experiments on two open-source realworld mobile network fraud datasets. The results show that CSGNN can effectively solve the graph imbalance problem and then achieve better detection performance than the state-of-the-art algorithms. We believe that our research can be applied to solve the graph imbalance problems in other fields. The CSGNN code and datasets are publicly available at https://github.com/xxhu94/CSGNN.