Verifiable Secret Sharing (VSS) is an important cryptographic primitive in distributed computing. The most of pervious VSS almost depended on the commitments which was established under the computational assumption of discrete algorithm problem which had been proofed unsecure. So a quantum-resistant VSS scheme which can be applied in secret sharing schemes implemented by different methods is called for. In this study, we analyze the existing verifiable sharing schemes. In order to solve the flaws in the existing schemes, we propose a new scheme with the applicability to secret sharing implemented by lattice cryptography. In addition, it has higher verification efficiency compared to past schemes and resistance so far to cryptanalysis by quantum algorithms.