Perception of trustworthiness of service providers is a fundamental need in service selection. Trust propagation has been used to predict trustworthiness of service providers in service-oriented social networks. However, existing trust propagation methods may suffer from a scalability problem, i.e., their computation time is likely too high to be acceptable in practice, especially when they are applied to very large-scale service-oriented social networks. Moreover, they rarely consider the structural properties of social networks to optimize their performance. This paper proposes an efficient trust propagation scheme for predicting trust in service-oriented social networks. It exploits the specific structural properties of social networks and builds an advanced data structure from preprocessing to improve the efficiency of trust propagation. Our scheme can support multiple trust propagation strategies. Experiments show that our scheme is much more efficient than well-known trust propagation methods in trust prediction, while its trust prediction results are as accurate as theirs in service-oriented social networks.