The patients of paralysis with motion impairment problems require extensive rehabilitation programs to regain motor functions. The great labor intensity and limited therapeutic effect of traditional human-based manual treatment have recently boosted the development of robot-assisted rehabilitation therapy. In the present work, a neural-fuzzy adaptive controller (NFAC) based on radial basis function network (RBFN) is developed for a rehabilitation exoskeleton to provide human arm movement assistance. A comprehensive overview is presented to describe the mechanical structure and electrical real-time control system of the therapeutic robot, which provides seven actuated degrees of freedom (DOFs) and achieves natural ranges of upper extremity movement. For the purpose of supporting the disable patients to perform repetitive passive rehabilitation training, the RBFN-based NFAC algorithm is proposed to guarantee trajectory tracking accuracy with parametric uncertainties and environmental disturbances. The stability of the proposed control scheme is demonstrated through Lyapunov stability theory. Further experimental investigation, involving the position tracking experiment and the frequency response experiment, are conducted to compare the control performance of the proposed method to those of cascaded proportional-integral-derivative controller (CPID) and fuzzy sliding mode controller (FSMC). The comparison results indicate that the proposed RBFN-based NFAC algorithm is capable of obtaining lower position tracking error and better frequency response characteristic.