With the rapidly increasing number of independently developed Web services that provide similar functionalities with varied quality of service (QoS), service composition is considered as a problem in the selection of component services that are in accordance with users' QoS requirements; a practice known as the QoS-aware service composition problem. However, current solutions are unsuitable for most real-time decision-making service composition applications required to obtain a relatively optimal result within a reasonable amount of time. These services are also unreliable (or even risky) given the open service-oriented environment. In this paper, we address these problems and propose a novel heuristic algorithm for an efficient and reliable selection of trustworthy services in a service composition. The proposed algorithm consists of three steps. First, a trust-based selection method is used to filter untrustworthy component services. Second, convex hulls are constructed to reduce the search space in the process of service composition. Finally, a heuristic global optimization approach is used to obtain the near-optimal solution. The results demonstrate that our approach obtains a close-to-optimal and reliable solution within a reasonable computation time.