In a universal designated multi-verifiers signature (UDMVS) scheme, any signature holder, not necessarily the signer, can non-interactively prove to a set of specific verifiers the fact that the signature holder holds a valid signature from the signer, but the designated verifiers are unable to convince any third party of this fact. However, the existing UDMVS schemes based on the large integer factorization problem and the discrete logarithm problem on finite field or elliptic curve are no longer secure in the post quantum era. To overcome this limitation, we propose a lattice-based UDMVS scheme, which is resistant to quantum computing attacks, it also avoids the risk of online eavesdropping attacks on existing universal designated verifier signature schemes. Moreover, based on the small integer solution (SIS) problem and the learning with errors (LWE) problem, the proposed lattice-based UDMVS scheme is provably secure in the random oracle model for the strong unforgeability, the non-transferability and the privacy of signer’s identity.