In this paper, a network organizing method with node alternate operation scheme is put forward for both prolonging the network lifetime and decreasing the number of nodes for determined deployment with concentric rings in wireless sensor networks (WSNs). With the method, each node is powered by a battery with an analytical non-linear model in consideration; the nodes for every deployment position is designed to operate alternately; accordingly, TDMA is applied for data transmission and reception from the nodes of the outermost layer to the sink deployed in the centre of circle; FSK is introduced for node energy efficiency; furthermore, non-uniform deployment with varied number of nodes in different layer is considered for network energy balance. For evaluating the performance of our proposed network organizing method, a method with simple node operation scheme is used for comparison. Simulation results show that, when the number of nodes deployed in the innermost layer is specified, our proposed method requires less number of nodes for the network deployment, simultaneously achieves longer network lifetime.