With the proliferation of online communities and Person-to-Person (P2P) online service markets, the deployment of knowledge, skills, experiences and user generated contents services are generally facilitated among service users and service providers. In online service markets where well-established intermediaries are often eliminated, the success of social interactions for service exchange among completely unknown users depends on ‘trust’ of a service user for a service provider. Therefore, providing a satisfactory trust model to evaluate the quality of services and to recommend personalized trustworthy service providers is vital for a successful online community and P2P online service market. However, finding trustworthy service providers for each individual user is challenging because of the lack of direct experiences and the subjective property of trust. In order to resolve the challenges, current research on trust prediction strongly relies on a web of trust, which is directly collected from users. However, the web of trust is not always available in online communities and, even when it is available, it is often too sparse to accurately predict the trust value between two unacquainted people. In this paper, we propose a computational trust model to predict trust connectivity based on service providers’ expertise (local trust from direct experiences and a reputation) and service users’ affinity for certain contexts (topics). The approach used item rating data that is available and much more dense than direct trust data. In experiments with a real-world dataset, we show that our model can predict trust connectivity with a high degree of accuracy. The proposed computational trust framework can be applied to any type of online communities or P2P online service markets with a rating system.