Digital signature is an important cryptographic tool in the security and privacy of smart city. Certificateless signature has not only simplified certificate management of traditional public-key signature, but also solved the private key escrow problem of ID-based signature. Recently, Pang et al.'s proposed a certificateless signature scheme in the standard model. We find that their scheme is vulnerable to the attack of maliciousbut- passive KGC adversary. From the analysis of Pang et al.'s secure proof, we give a suggestion for the proof of certificateless signature, i.e., we cannot remain some possible trapdoor information for KGC. Then we propose a strongly secure certificateless signature scheme, and give the secure proof in standard model. Compared with Pang et al.'s and other certificateless signature scheme in standard model, our proposed scheme can resist attack of malicious-but-passive KGC adversary.