In this study, a new fuzzy robust backstepping controller with estimation is proposed for the control of a robot manipulator. Backstepping control is preferred because the Lyapunov function that is used in stability analysis and the feedback control law that is used for control purpose are defined systematically during controller design. Fuzzy logic units are designed to update the gains of the backstepping controller. Then, the proposed controller is applied to a robot manipulator that is to track a trajectory in a three-dimensional space while it is subjected to external disturbances and parameter variations. The numerical results demonstrate and verify the successful performance of the proposed controller.