Ensuring the security of transmitted content is an important task in network communication. Signcryption technology combines signature and encryption operations in a single step to achieve message authentication and confidentiality. In practical applications, users are usually in different cryptographic systems, the ordinary signcryption technology cannot realize communication between two different cryptographic systems. And the ciphertext structure of the existing signcryption schemes is relatively complex, signcryption is not efficient. Therefore, in order to solve the problem of efficient communication between different cryptosystems and ensure quantum security, this paper proposes a lattice-based efficient heterogeneous signcryption scheme for secure network communications. This signcryption scheme accomplishes signcryption through matrix operations and hash functions, which avoids complex signcryption structures, efficiently realizes bidirectional message communication between identity-based cryptosystems and certificateless cryptosystems.