Based on the characteristics that the indirect relation can bring about the utility for individual in society, the transitivity of degree is introduced in the 'preferential connectivity' mechanism of BA model, and the model of social growing network is built. Theoretic analyses and simulation results show that the networks generated by current model display the property of degree distribution falling between the exponential distribution and scalefree distribution, and at the same time have the property of assortativemixing. Therefore, the transitivity of degree can explain the cause of formation for the properties of the degree distribution and the degree correlations of social networks.