Remote user authentication scheme is a kind of way to authenticate the communication parties who transmit messages through an insecure channel. Researchers in this area have proposed some approaches during the last couple of decades. Unfortunately, most of them are proved to be insecure against various attacks. In 2009, Kim and Chung improved Yoon and Yoo's scheme, and claimed that their scheme can prevent masquerading attack as well as resist to other malicious attacks. However, the authors found that Kim and Chung's scheme is still not secure enough, especially in preventing off-line password guessing attack. In this paper, they proposed a more secure and practical remote user authentication scheme to resolve all of the aforementioned security vulnerabilities while preserving the merits of Kim-Chung's scheme.