The traditional collaborative filtering recommendation algorithm has such problems as data sparseness, cold-start and new users. With the rapid development of social network and e-commerce, how to provide personalized recommendations based on the trust between users and user interest tag is becoming a hot research topic. In this study, we propose a probability matrix factorization model (STUIPMF) by integrating social trust and user interest. First, we excavate implicit trust relationship between users and potential interest label from the perspective of user rating. Then we use the probability matrix factorization model to conduct matrix decomposition of user ratings information, users trust relationship, user interest label information, and further excavate the user characteristics to ease data sparseness. Finally, we make experiments based on the Epinions dataset to verify the proposed method. The results show that the proposed method can to some extent improve the recommendation accuracy, ease cold-start and new user problems. Meanwhile, the proposed STUIPMF approach also has good scalability.