In an anonymous credential system, a user can obtain credentials from the organization and can prove the possession of credentials to the service providers, without leaking the privacy. There are three kinds of parties in the scheme: organization, service providers and users. In the previous works, the anonymous credentials schemes cannot prevent the collusion between the organization and the service providers from finding the users? privacy. In this paper, a scheme of anti-collusion anonymous credentials is proposed, it can be based on any secure public key algorithm. In the scheme, there doesn?t need a trusted third party to issue the public keys and the secret keys, the scheme take the advantage of the relation of the public key and the secret key, i.e., it is easy to generate a pair of public key and the corresponding secret key, but hard to deduce the secret key from a particular public key. Therefore, the participant only need to have the ability to generate a pair of public key and secret key.