A quantum computer is a paradigm of information processing that can show remarkable possibilities of exponentially improved information processing. However, this paradigm could disrupt the current cryptosystem, which is called quantum computing attacks, by calculating factoring problem and discrete logarithm problem. Recently, NTRU is applied to various security systems, because it provides security against to provide secu-rity against quantum computing attacks. Furthermore, NTRU provides similar security level and efficient computation time of encryption/decryption compared to traditional PKC. In 2018, Jeong et al. proposed an user authentication and key distribution scheme using NTRU. They claimed that their scheme provides various security properties and secure against quantum comput-ing attacks. In this paper, we demonstrate that their scheme has security pitfalls and incorrectness in login and authentication phase. We also suggest countermeasures to fix the incorrectness and provide security against various attacks.