Abstract: This paper develops a decentralized adaptive impedance control scheme for industrial robot working in task space. This controller does not require any knowledge of either structure or parameter values of robot dynamic model, it possesses a decentralized control structure and is computationally efficient, it have the properties of fault tolerance relative to centralized strategies and good robustness. The proposed control law is expressed in task space and is easy to apply to robot with degrees of redundancy. It is shown that the control strategy is globally uniformly bounded in the presence of bounded disturbances. Computation results are give for a PUMA 560 manipulators to demonstrate the good performance of the proposed scheme.