With the rapid development of blockchain technology, the hierarchical distributed authentication system has been widely adopted due to its efficient authentication and flexible authorization among multi-level nodes, but the traditional hierarchical authentication mechanism is based on classical cryptography, which is not able to resist the attack of quantum computers. Constructing an authentication mechanism using post-quantum cryptography is a reliable solution, such as lattice-based cryptography, etc. However, most of these approaches, while capable of providing quantum-resistant security, lack a hierarchical structure to efficiently support the need for authentication between multi-level nodes in a blockchain environment. In this paper, a Hierarchical distributed authentication scheme based on lattice cryptography is proposed. Specifically, the counter quantum property of lattice cryptography is utilized in conjunction with optimized non-interactive zero-knowledge proofs to design a multi-layer authentication process that guarantees the integrity of authentication information while reducing the communication overhead. The results show that the proposed method not only has significant advantages in resisting quantum attacks, but also effectively reduces the authentication delay and improves the overall efficiency of the system.