It is important for personalized social services to calculate the relationship strength between users in a social network. Meanwhile, the psychological studies has shown that the personality traits is one of the key factors affecting the user's relationship strength. Based on the relationship generation principle in the social psychology, this paper proposes a personality embedded social relationship strength hierarchical model and algorithm. With the analysis of a user's behavior in social network, this paper predicts the Big Five personality traits of the user to calculate the propensity of personality. The propensity of personality is combined with the similarity of preference and the familiarity of interaction to formalize the personality embedded user relationship strength calculation. At the end of this paper, the proposed algorithm is demonstrated to be reasonable and effective in a simulation experiment of RENREN social network.