As underwater monitoring technology is well-developed, the underwater sensor network plays an important role for the exploration of the oceans. But there exist possible risks of sensor nodes being captured by adversaries and the transmissions in the underwater communication being illegally accessed. As a result, it is vital to take the security issue into account in such an underwater mobile sensor network. In this paper, our goal is to propose a key distribution scheme adequate for underwater mobile sensor networks. We adopt a mobility model to capture the movement of the sensors floating on the sea. Our key distribution scheme is designed to fit the characteristics of the sensors' movement, and hence the connection and security can be improved in underwater sensor networks. Our scheme can also reduce redundant keys in the key distribution system. We also propose a secure routing method based on the Focused Beam Routing Protocol to adapt to our proposed iterative key distribution scheme. The simulation results show that our scheme possesses better performance, including better local connectivity, availability of path key, resilience and routing results.