Wireless rechargeable sensor networks are becoming crucial and important in recent years for the advancement of wireless energy transmission technology. The previous research shown that not all of sensors can be recharged due to the limitation of energy capacity that mobile chargers can carry. If a sensor playing a critical role in a sensing task cannot function as usual due to the exhausted energy, then the sensing task will be interrupted. Therefore, this paper proposes a novel recharging mechanism taking the priorities of sensors into consideration such that mobile chargers can recharge the sensor with a higher priority and the network lifetime can be efficiently sustained. The priority of each sensor depends on its contribution to the sensing task, including the coverage and connectivity capabilities. Based on the priority, the sensor with a higher priority will be properly recharged to extend the network lifetime. Simulation results show that the proposed mechanism performs better against the related work in network lifetime.