Digital signature, as an important crypto-graphic primitive, has been widely used in many ap-plication scenarios, such as e-commerce, authentica-tion, cloud computing, and so on. Certificateless Pub-lic Key Cryptography (PKC) can get rid of the cer-tificate management problem in the traditional Public Key Infrastructure (PKI) and eliminate the key-escrow problem in the identity-based PKC. Lately, a new Cer-tificateless Signature (CLS) scheme has been proposed by Kyung-Ah Shim (IEEE SYSTEMS JOURNAL, 2018, 13(2)), which claimed to achieve provable secu-rity in the standard model. Unfortunately, we present a concrete attack to demonstrate that the scheme can-not defend against the Type I adversary. In this type of attack, the adversary can replace the public key of the signer, and then he plays the role of the signer to forge a legal certificateless signature on any message. Furthermore, we give an improved CLS scheme to re-sist such an attack. In terms of the efficiency and the signature length, the improved CLS is preferable to the original scheme and some recently proposed CLS schemes in the case of precomputation.