Conventional remote user strong-password authentication schemes have the common drawback that the user has to memorize a hard-to-remember textual password, and therefore their applications are restricted. To solve this problem, we propose a remote user authentication scheme using strong graphical passwords in this paper. As graphical passwords are easy to remember for the user and conventionally dictionary attacks on graphical passwords are infeasible, the practicability of the proposed scheme is improved. Next, we show that the proposed scheme can withstand the replay attack, the password- file compromise attack, the denial-of-service attack, the predictable n attack, and the insider attack. In particular, the proposed scheme is easily reparable.