Generalized ring signcryption (GRSC) can realize ring signature and ring signcryption functions with only one key pair and one algorithm. It is very useful for a system with a large number of users, or whose function may be changed, or with limited storage space. We give a formal definition and security model of GRSC in the certificate-based cryptosystem setting and propose a concrete scheme by using bilinear pairings. The confidentiality of our scheme can be proved under the GBDH and CDH assumptions and the unforgeability of our scheme can be proved under [Formula: see text] and CDH assumptions in the random oracle model, and what is more, our scheme has unconditional anonymity. Compared with other certificateless ring signcryption schemes that use bilinear pairings, it is a highly efficient one.