Blind signature is a well-known cryptographical technique used to construct some advanced applications for the consideration of user privacy. In this work, we propose the first efficient certificate-based blind signature scheme that follows the idea of Certificate Based Encryption (CBE) presented by Gentry in EuroCrypt 2003. The security of our scheme is based on the elliptic curve discrete logarithm problem over a finite field. In addition, our scheme does not require any pairing operations which is regarded as cosely operations compared to other operations. Compared with the other secure blind signature scheme, our scheme enjoys shorter signature length, less running time and operation cost. So it can be used widely, especially in low-bandwidth communication environments such as wireless cooperative networks.