Topologies with energy-efficient and strong invulnerability has become an important issue in the development of Wireless Sensor Networks (WSNs). In this paper, we propose a Poisson-growth model based on regulated attractiveness function to build a WSN with scale-free topology, named PSFBRA. In the model, adjustable parameters are introduced for balancing connectivity and energy consumption in WSNs. Then a mathematical optimization model which based on the endurable probability and the topology structure entropy is established. Through analyzing the values of the topologic parameters, the optimal scaling exponent of the PSFBRA topology is obtained. Finally, simulation results show that PSFBRA topology is more in line with the practical application of WSNs, maintains the fault tolerance of scale-free network under random failures, improves the network invulnerability under intentional attacks and effectively enhances the communication efficiency.