Identity-based cryptosystem has many advantages over PKI-based cryptosystem in key distribution, but key escrow is always an inherent drawback. In order to solve the problem, certificateless public key cryptography was introduced by Al-Riyami and Paterson in {8}. In this paper, we first introduce a certificateless signature scheme secure against both malicious PKG attack and DODattack without random oracle, which is the first scheme satisfying theses properties in the literature. Based on the certificateless signature scheme, we also present a constant-size group signature scheme against malicious group manager.