A critical issue in wireless sensor networks is an energy-efficiency since the sensor batteries have limited energy power and, in most cases, are not rechargeable. The most practical manner relate to this issue is to use a node wake-up scheduling protocol that some sensor nodes stay active to provide sensing service, while the others are inactive for conserving their energy. Especially, CTC (Connected Target Coverage) problem has been considered as a representative energy-efficiency problem considering connectivity as well as target coverage. In this paper, we propose a new energy consumption model considering multiple-targets and create a new problem, CMTC (Connected Multiple-Target Coverage) problem, of which objective is to maximize the network lifetime based on the energy consumption model. Also, we present SPT (Shortest Path based on Targets)-Greedy algorithm to solve the problem. Our simulation results show that SPT-Greedy algorithm performs much better than previous algorithm in terms of the network lifetime.