An anonymous credential system allows a user to convince a verifier of the possession of user's attributes anonymously. A range proof protocol in an anonymous credential system is the protocol where the user can show that user's attribute belongs to a certain integer range without revealing the attribute. In the previous scheme, while the constant computational complexity is achieved, the size of the public parameters depends on the number of the attributes N. This paper proposes a range proof protocol with O (logTV) public parameter size. We also implement and evaluate it.