An anonymous credential system allows the user to convince a verifier of the possession of a certificate issued by the issuing authority anonymously. One of the applications is the privacy-enhancing electronic ID (eID). A previously proposed anonymous credential system achieves constant complexity in the number of finite-set attributes of the user. However, the system is based on the RSA. In this paper, we show how to achieve the constant complexity in a pairing-based anonymous credential system excluding the RSA. The key idea of the construction is the use of a pairing-based accumulator. The accumulator outputs a constant-size value from a large set of input values. Using zero-knowledge proofs of pairing-based certificates and accumulators, we can prove AND and OR relations with constant complexity in the number of finite-set attributes.