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, efficient and achieves the other desired functionality. In our 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 his password himself freely at the time of registration and can also change his password anytime without connecting to the server. The proposed scheme also solves the serious time synchronization problem. The proposed scheme appeals for practical implementation as far as its achievements and resistance to various attacks are concerned.