Recently, the certificateless public key cryptography (CLPKC) has been studied widely since it could solve both of the certificate management problem in traditional public key cryptography (TPKC) and the key escrow problem in the identity-based public key cryptography (ID-based PKC). To satisfy requirements of different applications, many certificateless blind signature (CLBS) schemes using bilinear pairing for the CLPKC setting have been proposed. However, the bilinear pairing operation is very complicated. Therefore, the performance of those CLBS schemes is not very satisfactory. To solve the problem, we propose an efficient CLBS scheme without bilinear pairing. Performance analysis shows that the proposed scheme could reduce costs of computation and storage. Security analysis shows the proposed scheme is provably secure against both of two types of adversaries.