Increasingly, social network datasets contain social attribute information about actors and their relationship. Analyzing such attribute-rich social networks requires making sense of not only its structural features, but also the relationship between social attributes and network structures. Existing social network analysis tools are usually weak in supporting complex analytical tasks involving both structural and social attributes, and often overlook users' needs for sensemaking tools that help to gather, synthesize, and organize information. To address these challenges, we propose a sensemaking framework of social-network visual analytics in this paper. This framework considers both bottom-up processes, which are about constructing new understandings based on collected information, and top-down processes, which concern using prior knowledge to guide information collection, in analyzing attribute-rich social networks. The framework also emphasizes the externalization of sensemaking processes through interactive visualization. Guided by the framework, we develop a system, SocialNetSense, to support the sensemaking in visual analytics of attribute-rich social networks.