Aiming at distinguishing service credibility in the largescale distributed cloud computing system, we propose a relevanceaware cloud service trust model based on convex evidence theory. The model formally describes the trust relationship among service providers, services and users in the cloud computing system. Then, the correlation between different services from the same service provider is revealed. Furthermore, the model uses the convex evidence theory to deal with ordered propositions and finally builds a credible service recommendation method for the cloud computing system, which can provide reasonable and reliable cloud services for users according to user needs. Through the comparison with the classical evidence theory, the experimental results demonstrate the validity and robustness of the relevanceaware cloud service trust model based on convex evidence theory while can make full use of correlation information among cloud services in the cloud computing system and provide reasonable cloud services according to user requests.