Existing models often uncovered the evolution patterns via statistical analysis，which would be unable to explain micro behavior reasons driving the social network evolution． To make up the deficiency，a utility function of network individuals is established and a utility analysis is introduced to model the social network evolution． Meanwhile，the meeting sequence，embedded in the social network evolution，is further modeled as a latent variable in order to explain the evolution phenomenon that the mentioned utility analysis cannot explain． Subsequently，taking one-period observation of social network structure and individual attributes as the input，a Bayes-inference-based method is developed for estimating the preference parameters and the latent meeting states． Through two groups of simulation analysis，the accuracy of parameter estimation and the applicable scope are verified，and the proposed model is also applied to validate its explanatory power and predictive force on the collected real data from Facebook platform． In all，the proposed model will be helpful to explain how social network forms on social media platforms and also to predict the tendency of social network evolution， so that it can lay a foundation for achieving the expected network structure and further controlling the information spreading within social networks．