In conventional ID-based user authentications, privacy issues may occur, since users' behavior histories are collected in Service Providers (SPs). Although anonymous authentications such as group signatures have been proposed, these schemes rely on a Trusted Third Party (TTP) capable of tracing misbehaving users. Thus, the privacy is not high, because the TTP of tracing authority can always trace users. Therefore, the anonymous credential system using a blacklist without the TTP of tracing authority has been proposed, where blacklisted anonymous users can be blocked. Recently, an RSA-based blacklistable anonymous credential system with efficiency improvement has been proposed. However, this system still has an efficiency problem: The data size in the authentication is O(K'), where K' is the maximum number of sessions in which the user can conduct. Furthermore, the O(K')-size data causes the user the computational cost of O(K') exponentiations. In this paper, a blacklistable anonymous credential system using a pairing-based accumulator is proposed. In the proposed system, the data size in the authentication is constant for parameters. Although the user's computational cost depends on parameters, the dependent cost is O(δ_BL·K) multiplications, instead of exponentiations, where δ_BL is the number of sessions added to the blacklist after the last authentication of the user, and K is the number of past sessions of the user. The demerit of the proposed system is O(n)-size public key, where n corresponds to the total number of all sessions of all users in the system. But, the user only has to download the public key once.