Signcryption is a cryptographic primitive that fulfills both the functions of digital signature and public key encryption simultaneously, at a cost significantly lower than that required by the traditional signature-then- encryption approach. Signcryption has been shown to be useful in many applications, such as electronic commerce, mobile communications and smart cards. Recently, three identity-based signcryption schemes in the standard model were proposed. However, the three schemes are broken soon. How to construct a secure identity-based signcryption scheme in the standard model is still an open problem. In this paper, we solve this problem and propose an efficient identity-based signcryption scheme in the standard model. We prove that our scheme has the indistinguishability against adaptive chosen ciphertext attacks under the modified decisional bilinear Diffie-Hellman assumption and the existential unforgeability against adaptive chosen messages attacks under the computational Diffie-Hellman assumption.