In this paper, a novel Mobile-Coverage scheme is proposed to improve the coverage and lifetime of hybrid sensor networks, and thus the target region can be completely covered with minimum number of mobile sensor nodes and the energy consumption can be reduced in hybrid sensor networks at the same time. Our scheme is applied to a hybrid network comprising of both static and mobile sensor nodes, which are randomly deployed in a rectangle area. We derived the minimum number of sensor nodes as well as the mobile nodes required to cover the target region completely. Compared to the existing works, the minimum number of mobile sensor nodes required in this paper is significantly smaller, which implies that the movement distance and energy consumption of mobile nodes in our scheme is reduced. Moreover, we proved that the construction of our scheme based on the Virtual Force and Voronoi Graph (VFVG) is correct, and then derived the optimal trade-off between the coverage of the target region and energy consumption of mobile nodes. Our scheme can achieve the maximum coverage which is 98.7% by minimum number of mobile sensor nodes. Meanwhile, a connectivity rate of 76.84% can also be achieved by our connectivity evaluation method. Finally, a new topology construction algorithm-Topology Construction and Maintenance based on Trust (TCMT) is created to further increase the lifetime of the sensor network. We also evaluated the performance of our scheme in terms of coverage and lifetime, and carried out extensive experiments to compare the coverage and energy consumption in our scheme and several previous schemes. The experimental results showed that our scheme is more efficient than the previous schemes simulated. INDEX TERMS Topology construction and maintain, Minimum numbers of mobile sensor, Voronoi graph, Virtual force, TCMT.