The computer networks have made possible to access data remotely and they have made possible to login into a system located at far distance; it may be in a different city or in a different country other than the user’s native place. The main issue in such an environment is related to the authenticity of the user’s identity by the system. This requires to have some mechanism to authenticate a remote user for his legitimacy. In this paper, we propose a method, which is based on a 3-D Geometric approach, to authenticate the login request sent by a user, who is located at far distance. In this method, we provide two-way mutual authentication in which a legitimate user is authenticated by the server and the server is authenticated by the user. This method first performs initialization in which the required parameters are set to create an environment with the central authority. It then allows a user to register with the system/server. Once a user is registered, he is allowed to login to the system for accessing the required information. Our scheme provides a facility to a legitimate user for changing his password of his choice. This scheme withstands with several attacks without requiring much computational overhead.