The blind signature schemes are useful in some applications where the anonymity is a thorny issue. The certificateless public key cryptography (CL-PKC) can eliminate the certificate management problem and solve the key escrow problem. In this paper, we put forward a secure and efficient CLBS scheme. We then illustrate that our new scheme is secure in the random oracle model. Also, we theoretically validate that our proposed scheme is more efficient than those existing ones in terms of computational complexity. We hope to transfer our scheme into applications.