Online/offline signcryption can not only enhance the computation efficiency of mobile devices, but also ensure the confidentiality and unforgeability of data simultaneously. Under the heterogeneous cryptography environment, the online/offline heterogeneous signcryption between different public key cryptographies should be taken into consideration. We define the online/offline heterogeneous signcryption security model from certificateless public key cryptography (CLPKC) to identitybased public key cryptography (IDPKC), and propose a concrete online/offline heterogeneous signcryption scheme from CLPKC to IDPKC. When performing signcryption operation, the scheme does not require any billinear pairing operation. Besides, it only needs two billinear pairing operations when performing unsigncryption. Compared with existing online/offline heterogeneous signcryption schemes, the proposed scheme has no certificate management problem while having equivalent efficiency, and thus it is suitable for mobile devices with limited computing power. The security proof shows that the scheme can meet the need of confidentiality and unforgeability. We analyze the efficiency of of online/offube signcryption and unsigncryption of the proposed scheme in the simulation step. The scheme adopts independent system parameters, which makes it more suitable for practical application environments.