Certificate less public key cryptography is an attractive paradigm since it eliminates the use of certificates in traditional public key cryptography and alleviates the inherent key escrow problem in identity-based cryptography. Recently, Xiong et al. Proposed a certificate less signature scheme and proved that their scheme is existentially unforgeable against adaptive chosen message attack under the random oracle model. He et al. Pointed out that Xiong et al.'s scheme is insecure against the Type II adversary. But, their forged signatures are not random, and their improved scheme has the same security defects as Xiong et al.'s scheme. In this paper, we present two malicious-but-passive KGC attack methods on Xiong et al.'s scheme and our results show that their scheme is insecure against malicious-but-passive KGC attack. We also propose an improved scheme which is secure against the super Type I adversary and super Type II adversary.