Human life is in a complex network world. In everyday life, the network can be a physical object such as the Internet, power network, road network and neural network; can also abstract not touch, such as interpersonal networks, networks of co-operation in scientific research, product supply chain network, biological populations, networks, etc.. The topology of these networks, the statistical characteristics and the formation mechanism, and so on, has a very important significance for the efficient allocation of resources, provides various functions, as well as the stability of the network, however, due to the complexity of these networks, conventional simplified model and cannot be good solution to the above problems. The complex network and network complexity has become a hot issue in the scientific and engineering concern. This article describes a few common complex network models and its application brief.