Complex network theory is used for depicting and investigating structures and functions of natural and artificial social networks or systems. Current state-of-the-art research is limited to either modeling Wireless Sensor Networks (WSNs) under some energy constraint or assuming fixed/static network model. However, WSNs is a dynamic social network, it should be an evolution network, and time of the sensor nodes adding to the network cannot be uniform. In this paper, we try to explore the Poisson dynamics of WSNs based on complex network theory combined with fitness function. Early works have not considered the node energy, we present a new Poisson-fitness model. Then we conduct theoretical analysis by using statistical physics approach. With numerical simulations, the results show that the model fits well with expect goals. Our results offer important references on the performance issues depending on specific application scenarios of WSNs.