Abstract: Signcryption is a cryptographic primitive that combines both the function of digital signature and encryption in a logical single step. However, in some occasion there are conflicts of interest between the two entities, so concurrent signature is proposed to ensure fair exchange of the signature without special trusted third party. The notion of concurrent signcryption is defined and the security model is proposed in this paper. And an identity-based concurrent signcryption scheme is established using bilinear based on the framework. The scheme is proved to be secure assuming Bilinear Diffie-Hellman problem and Computational Co-Diffie-Hellman problem are hard in the bilinear context.