Remote user authentication scheme is one of the simplest and the most convenient authentication mechanisms to deal with secret data over insecure networks. These types of schemes are applicable to the areas such as computer networks, wireless networks, remote login systems, operation systems and database management systems.The goal of a remote user authentication scheme is to identify a valid card holder as having the rights and privileges indicated by the issuer of the card. In recent years, so many remote user authentication schemes have been proposed to authenticate a legitimate user, but none of them can solve all possible problems and withstand all possible attacks. This paper presents a secure remote user authentication scheme with smart cards. The proposed scheme provides the essential security requirements and achieves particular attributes.