In anonymous reputation systems, where after an interaction between anonymous users, one of the user evaluates the peer by giving a rating. Ratings for a user are accumulated, which becomes the reputation of the user. By using the reputation, we can know the reliability of an anonymous user. Previously, anonymous reputation systems have been proposed, using an anonymous e-cash scheme. However, in the e-cash-based systems, the bank grasps the accumulated reputations for all users, and the fluctuation of reputations. These are private information for users. Furthermore, the timing attack using the deposit times is possible, which makes the anonymity weak. In this paper, we propose an anonymous reputation system, where the reputations of users are secret for even the reputation manager such as the bank. Our approach is to adopt an anonymous credential certifying the accumulated reputation of a user. Initially a user registers with the reputation manager, and is issued an initial certificate. After each interaction with a rater, the user as the ratee obtains an updated certificate certifying the previous reputation summed up by the current rating. The update protocol is based on the zero-knowledge proofs, and thus the reputations are secret for the reputation manager. On the other hand, due to the certificate, the user cannot maliciously alter his reputation.