Identity-based signcryption schemes based on large integer factorization and discrete logarithm problems were considered to be insecure for the quantum computer attack. Thus, choosing a quantum-resist platform and constructing secure schemes based on new hard assumptions are challenges. In this paper, we propose an alternative scheme - an identity-based signcryption on lattice, which does not need to rely on a trapdoor. Meanwhile, our scheme achieves IND-CCA2 and sUF-CMA security, and it is also secure against the current quantum algorithm attacks based on LWE problem for lattice. Furthermore, we demonstrate that the newly proposed scheme has much shorter secret key size, and higher speeds in signcryption and unsigncryption stages, compared with some exiting identity-based signcryption schemes.