Cloud computing is combination of various computing entities, globally separated, but electronically connected. As the geography of computation is moving towards corporate server rooms, it bring more issues including security, such as virtualization security, distributed computing, application security, identity management, access control and authentication. However, strong user authentication is the paramount requirement for cloud computing that restrict illegal access of cloud server. In this regard, this paper proposes a strong user authentication framework for cloud computing, where user legitimacy is strongly verified before enter into the cloud. The proposed framework provides identity management, mutual authentication, session key establishment between the users and the cloud server. A user can change his/her password, whenever demanded. Furthermore, security analysis realizes the feasibility of the proposed framework for cloud computing and achieves efficiency.