Trust management is one of the most challenging issues in the emerging cloud computing. A distributed way is adopted to manage and store trust feedbacks data. We propose a credibility-based trust management model that not only distinguishes between credible trust feedbacks, but also has the ability to detect the malicious trust feedbacks from attackers .On this basis, we also present a replication determination model that dynamically decides the optimal replica number of the trust management service so that the trust management service can be always maintained at a desired availability level. The research results have been validated by experimental results.