In order to extend the models and exploit new features for complex networks,the statistical properties of random complex networks are explored.In the investigation,first,on the basis of the Penrose tiling composed of two kinds of rhombus,random connections of the vertex are added to construct a partially random complex network in which the connecting probability depends on the vertex type.Then,the main characteristic parameters of the network are calculated by using analytical and numerical methods.It is found that the degree distribution,the ave- rage inter-node distance and the cluster coefficient of the partially random complex network are all close to those of general random networks but obey different variation laws,which means that the proposed quasi-periodic complex network possesses not only the common properties of general networks but also abundant specific features.