To assist or rehabilitate individuals with impaired upper-limb function, we have developed an upper-limb exoskeleton robot, the ETS-MARSE (motion assistive robotic-exoskeleton for superior extremity). The MARSE has seven degrees-of-freedom (DoFs) and is designed to be worn on the lateral side of upper limb. It is able to assist with shoulder, elbow and wrist joint movements. In this paper we implemented a trajectory tracking algorithm using a nonlinear sliding mode controller (SMC). To eliminate the chattering of conventional SMC, we employed the concept of boundary layer technique. Experimental results show that the SMC can effectively maneuver the developed MARSE to follow the reference trajectory.