Accurate prediction of user behaviors is important for many social media applications, including social marketing, personalization, and recommendation. A major challenge lies in that although many previous works model user behavior from only historical behavior logs, the available user behavior data or interactions between users and items in a given social network are usually very limited and sparse (e.g., ≥99.9% empty), which makes models overfit the rare observations and fail to provide accurate predictions. We observe that many people are members of several social networks in the same time, such as Facebook, Twitter, and Tencent's QQ. Importantly, users' behaviors and interests in different networks influence one another. This provides an opportunity to leverage the knowledge of user behaviors in different networks by considering the overlapping users in different networks as bridges, in order to alleviate the data sparsity problem, and enhance the predictive performance of user behavior modeling. Combining different networks "simply and naively" does not work well. In this article, we formulate the problem to model multiple networks as "adaptive composite transfer" and propose a framework called ComSoc. ComSoc first selects the most suitable networks inside a composite social network via a hierarchical Bayesian model, parameterized for individual users. It then builds topic models for user behavior prediction using both the relationships in the selected networks and related behavior data. With different relational regularization, we introduce different implementations, corresponding to different ways to transfer knowledge from composite social relations. To handle big data, we have implemented the algorithm using Map/Reduce. We demonstrate that the proposed composite network-based user behavior models significantly improve the predictive accuracy over a number of existing approaches on several real-world applications, including a very large social networking dataset from Tencent Inc.