For a group of mobile agents, each agent can sense the local environment around it and directly communicate with others in its communication range. This article deals with the self-deployment problem of mobile agents to achieve a sensing coverage over the environment as large as possible, while keeping the underlying time-variant communication topology connected all the time. For this problem, a self-deployment algorithm is developed for each agent. It guarantees network connectivity by preserving the group core structure, which is extracted from the communication topology in a completely distributed, local manner and is renewed in each iteration period. Note that maintaining all the connecting edges in the core structure still remains a sufficient degree of freedom for each agent to traverse over a maximal distance from its neighbours. Thus, the distributed connected coverage objective can be achieved by spreading out the group members with the constraints of preserving the core structure. The performance of the self-deployment algorithm is demonstrated by both theoretical analysis and numerical simulations.