In this paper, a problem of connected dynamic coverage is investigated for mobile sensor networks (MSNs), where a group of sensors (or agents) acts to monitor large areas of interest (AoI) while maintaining connectivity. This problem presents a delicate trade-off between connectivity and decreasing overlapping of sensing coverage. Motivated by the nature-inspired control method to solve the distributed problem, a selected interaction swarming algorithm is proposed to the connected dynamic coverage problem. First, it is proved that global connectivity can be preserved by preserving all subgroups’ connectivity at any adjacent moments. Based on the proof, a local interaction law is designed to develop a neighbor set of each agent. Besides, a pheromone mechanism is introduced to minimize the overlap of sensing coverage and maximize area coverage for each agent. Moreover, based on the local interaction law and pheromone mechanism, a distributed coverage control protocol is designed for dynamic coverage control and maintain connectivity. Numerical simulations are performed to demonstrate the effectiveness of the proposed algorithm.