Biological neural networks have dual properties of small-world attributes and scale-free attributes. Most of the current researches on neural networks are based on small-world networks or scale-free networks with lower clustering coefficient, however, the real brain network is a scale-free network with small-world attributes. In this paper, a scale-free spiking neural network with high clustering coefficient and small-world attribute was constructed. The dynamic evolution process was analyzed from three aspects: synaptic regulation process, firing characteristics and complex network characteristics. The experimental results show that, as time goes by, the synaptic strength gradually decreases and tends to be stable. As a result, the connection strength of the network decreases and tends to be stable; the firing rate of neurons gradually decreases and tends to be stable, and the synchronization becomes worse; the local information transmission efficiency is stable, the global information transmission efficiency is reduced and tends to be stable, and the small-world attributes are relatively stable. The dynamic characteristics vary with time and interact with each other. The regulation of synapses is based on the firing time of neurons, and the regulation of synapses will affect the firing of neurons and complex characteristics of networks. In this paper, a scale-free spiking neural network was constructed, which has biological authenticity. It lays a foundation for the research of artificial neural network and its engineering application.