This paper proposes a proxy-based proactive caching approach for enhancing consumer mobility in Content Centric Networks (CCN). The approach requests proactively and caches the contents that a user does not receive but is requested before a handover process. Compared with other approaches for consumer mobility, the analytical and simulation results indicate that the proposed approach has shorter handover delay and less average content retrieval time. In addition, the proposed approach costs less in retrieving content for mobile users. This approach can also support efficient content sharing in mobile CCN environments and alleviate negative effects of consumer mobility on real-time services.