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The node deployment in mobile sensor networks (MSNs) is mostly performed in a random method. However, a large number of redundant nodes may exist due to the randomness. As a result, severe data congestion may be caused and the quality of coverage (QoC) is undermined. In order to solve this QoC problem, we propose an Energy-efficient Nonlinear Coverage Control Protocol (ENCP). This protocol utilizes the normal distribution to calculate the minimal number of sensors which is required to guarantee coverage over the monitoring area. We also balance the node energy consumption and achieve the collaborative scheduling among all the sensor nodes. Meanwhile, when a certain QoC is guaranteed, we present the calculation model for the normal distribution of the sensing ranges and the proportional relationship between different parameters in the QoC function. Finally, simulation results show that the ENCP could not only improve the network QoC and network coverage rate but also effectively control the energy exhaustion at the nodes. Therefore, the network lifetime can be effectively prolonged. [ABSTRACT FROM AUTHOR]