On the basis of the fact that points on a unit sphere are easy to compute but hard to derive, this paper presents a remote login authentication scheme with smart card based on unit sphere. The proposed scheme is simple, secure, and efficient and achieves the other desired functionality. In the authors' scheme, a verification table is not stored at the server to authenticate users. The proposed scheme not only provides mutual authentication between the user and server, but also establishes a common session key to provide message confidentiality. In the proposed scheme, the user selects the password themselves freely at the time of registration and can also change their password anytime without connecting to the server.