The traditional digital multi-signature schemes are mostly based on large integer factorization and the discrete logarithm,which cannot be secured in quantum environment.The paper presents a lattice-based multi-signature scheme that can resist the quantum attack using the hardness of average-case short integer solution problem(SIS).Multi-signature includes the simultaneous signature and sequential signature.The paper describes respectively the key generation,multi-signature generation and multi-signature verification of the two types of schemes.Moreover,experimental results prove that the digital multi-signature scheme based on lattice is especially efficient and secure to multi-signature generation.