Abstract: Due to eliminating the inherent key escrow in identity-based cryptosystem and yet not needing certificates to guarantee the authenticity of public keys, the concept of certificateless public key cryptosystem is introduced. In this paper, a new certificateless signature scheme based on bilinear pairings is present. The signing algorithm of the proposed scheme is very simple and does not require any pairing computation, and the verification algorithm only needs three pairings computation. Furthermore, the scheme does not need special hash function. Our proposed scheme is more efficient than all knowing schemes in terms of computation overhead.