In social networks, recommender systems can help users to deal with information overload and provide personalized recommendations to them. The trust relationship of users is used in the social networks' recommender systems. But the state-of-art algorithms only use the single trust relationship which cannot capture the trust to user's friends when looking for different items. This paper proposes a topic-based trust recommendation algorithm using tensor factorization model. As the social information changes rapidly, the state-of-art algorithms often need redo factorization. To address the issue, the paper also presents an effective incremental method to adaptively update its previous factorized components rather than re-computing them on the whole dataset when the data changes. Experiments show that the proposed method can achieve better performance and the incremental method is suitable for the rapid changes in the social networks.