Coverage is one of the important performance indexes in wireless sensor networks. When the target is covered by k degrees by the sensor, more redundant data are generated, which may lead to network congestion, thus reducing the communication and coverage of the network and leading to a rapid depletion of energy. Therefore, this paper presents an energy balance and coverage control algorithm for the overlay network model based on node position relations. Areas are given by the analysis of the overlay network model. In terms of energy consumption, nodes with low energy consumption are scheduled by a given proportion of expected functions between the working nodes and the neighboring nodes, which balances the energy consumption of the entire network and optimizes network resources. Finally, the simulation results show that the proposed k-degree coverage algorithm not only improves the coverage quality of the network but also reduces the rapid energy consumption and prolongs the service life of the network.