The scarcity problem in user-product matrix has become severe, which is affecting the recommendation system efficiency in mobile services; it is also related to social networks and Internet of Things, where huge amount of data and complex relationships exist. This paper proposes a novel recommendation approach based on social relationships between users to handle the scarcity problem and facilitate recommendations in mobile services. We define a model of social relationships based on a set of call detail record factors of telecom users and design a vacancy-filling method to reduce the scarcity of the user-product matrix. An integrated similarity measure is provided to improve the filtering rules of neighbours of the target user. Then, we build a new recommendation system based on social relationships, with mobile services in the telecom industry as the application. Furthermore, we conductexperiments with the real-world data of voice calls, and experimental results show that the filling method proposed can effectively reduce the scarcity of the user-product matrix and our social relationships approach outperforms the collaborative filtering in terms of the call, precision and mean absolute error indicators.