With the advancement of internet network technologies, remote user authentication schemes using smart cards have been widely adopted. In order to satisfy the requirements of a remote user authentication scheme, the smart card has become an essential device, one that is widely used because of its low computational cost and expedient portability. Recently, Li et al. pointed out some security weaknesses in Chen et al.'s scheme, such as forward secrecy and the wrong password login problem, and proposed an enhanced user password authentication scheme based on smart card. However, we found weaknesses in their scheme. Accordingly, we propose an enhanced scheme to remedy these security weaknesses, and prove that our scheme is more secure and efficient for network application with several positive properties.