Certificate-based encryption was introduced in Eurocrypt'03 to solve the certificate management problem in public key encryption. Recently, this idea was extended to certificate-based signatures. Several new schemes and security models of certificate-based signatures have been proposed. In this paper, we first take a closer look at the certificate-based signature by comparing it with digital signatures in other popular public key systems. We introduce a new security model of certificate-based signature, which defines several new types of adversaries against certificate-based signatures, along with the security model of certificate-based signatures against them. The new model is clearer and more elaborated compared with other existing ones. We then investigate the relationship between certificate-based signatures and certificateless signatures, and propose a generic construction of certificate-based signatures. We prove that the generic construction is secure (in the random oracle model) against all types of adversaries defined in this paper, assuming the underlying certificateless signatures satisfying certain security notions. Based on our generic construction, we are able to construct new certificate-based signature schemes, which are more efficient in comparison with other schemes with similar security levels.