In this paper, we propose a new notion called Certificate Based Ring Signature (CBRS) that follows the idea of Certificate Based Encryption (CBE) presented by Gentry in EuroCrypt 2003. It preserves the advantages of CBE such as implicit certificate and no private key escrow. At the same time it inherits the properties of normal ring signature such as anonymity and spontaneity. We provide its security model and a concrete implementation. In addition, we also propose a variant of CBRS, called Certificate Based Linkable Ring Signature (CBLRS). It is similar to CBRS, except with linkability. That is, it allows the public to verify whether two given signatures are generated by the same signer, yet preserves the anonymity of this user. It can be seen as the Certificate Based version of normal linkable ring signature.