Signcryption has clear advantage over traditional sign-then-encrypt schemes. However, the computational overhead for signcryption is still too heavy when it is applied to resource-constraint systems. In this paper, we propose a generic construction of the identity-based online/offline signcryption, where most of computations are carried out when the associated message is still unavailable and the online part of our scheme does not require any exponent computations and therefore is very efficient. Our scheme isgeneric and identity-based, in the sense it is independent of the selection of signature and encryption algorithms. Our scheme possesses the properties of ciphertext indistinguishability (IND-gCCA2) and existentially unforgeability (UF-CMA).