Efficient energy management becomes a critical design issue for complex WSN (Wireless Sensor Network). Most of complex WSN employ the sleep mode to reduce the energy dissipation. However, it should cause the reduction of sensing coverage. This paper presents new wake-up algorithm for reducing energy consumption in complex WSN. The proposed wake-up algorithm is devised using geometric probability. It determined which node will be waked-up among the nodes having overlapped sensing coverage. The only one sensor node will be waked-up and it is ready to sense the event occurred uniformly. The simulation results show that the lifetime is increased by 15% and the sensing coverage is increased by 20% compared to the other scheduling methods. Consequently, the proposed wake-up algorithm can eliminate the power dissipation in the overlapped sensing coverage. Thus, it can be applicable for the various WSN suffering from the limited power supply.