Concerning the problem that most of the existing social network growing models have negative degree correlation, considering the characteristics of positive degree correlations and high clustering coefficients, a new social network growing model was proposed based on Holme and Kim (HK) model. Firstly, the topological structure of a real-world social network was analyzed to obtain some important topological parameters of real social networks. Secondly, the HK model was improved by introducing triad formation mechanism, namely HK extended model with Turnable Degree Correlation and Clustering coefficient (HK-TDC&C), by which both clustering coefficients and degree correlations in the network could be adjusted. The model could be used to construct social networks with various topological properties. Finally, using mean field theory, the degree distribution of the model was analyzed, and Matlab was used for numerical simulation to calculate other topological parameters of the network. The results show that, by turning preferred attachment parameters and connection probabilities, the social network constructed by HK-TDC&C model can satisfy the basic characteristics of social networks, including scale-free characteristics, small world characteristics, high clustering coefficient characteristics and degree positive correlation properties, and its topology is closer to the real social network.