Robot manipulator has highly nonlinear dynamics. Therefore the control of multi-link robot arms is a challenging and difficult problem. In this paper an independent joint adaptive fuzzy sliding mode scheme is developed leer control of robot manipulators. The proposed scheme does not require an accurate manipulator dynamic model, yet it guarantees asymptotic trajectory tracking despite gross robot parameter variations. Numerical simulation for independent joint control of a 3-axis PUMA arm will also be included.