We propose and formally characterize a new problem named the dynamic context coverage problem in capabilityconstrained mobile sensor network environments. The goal is to move and adjust a network of mobile sensors with limited sensing capabilities to quickly achieve good coverage of dynamic changing contexts and continuously maintain the level of coverage. We propose several self-organization strategies and algorithms to solve the problem. Simulation results demonstrate that our techniques are highly efective in terms of dynamic context coverage, moving distance and self-organized deployment patterns.