Remote user authentication scheme is one of the most convenient authentication schemes to deal with secret data over insecure channel. During the last couple of decades, many researchers have proposed a remote user authentication schemes which are ID- based, password-based, and smart card-based. Above all, smart card-based authentication schemes are becoming day by day more popular. One of the benefits of smart card-based authentication scheme is that a server does not have to keep a password table. In 2013, Jin et al. improved Kim and Chung's scheme, and claimed that their scheme is more secure and practical remote user authentication scheme. However, we found that Jin et al.'s scheme is still insecure and vulnerable to smart card stolen attack. In this paper, we propose an improved remote user authentication scheme which is aimed to withstand this attack. Then, we show that the proposed scheme is more secure and supports security properties.