With the rapid development of quantum theory, the discrete logarithm problem and significant integer factorization problem have polynomial solution algorithms under quantum computing, and their security is seriously threatened. Therefore, a three-party password-authenticated key agreement scheme based on module learning with errors problem was proposed, and its security was proved in the BPR model. Compared with other password-authenticated key agreement protocols, the proposed protocol has higher efficiency and a shorter key length, which can resist quantum attacks. Therefore, the protocol is efficient and secure and suitable for large-scale network communication.