In this paper, we use master equation and continuum theory approach to investigate a number of problems in complex networks. The paper improves some extending to BA scale-free network model's algorithm. This paper provided a kind of scale-free networks model attractive factor by random, which analyzed degree distribution as well as the range of significant influence to degree distribution. The results of computer simulation were in concordance with the theoretical analysis. It is a scale-free networks. The new model could reflect some important characters of actual networks well and has application value.