Previous studies on robotic rehabilitation have shown that subjects’ active participation and effort involved in rehabilitation training can promote the performance of therapies. In order to improve the voluntary effort of participants during the rehabilitation training, assist-as-needed (AAN) control strategies regulating the robotic assistance according to subjects’ performance and conditions have been developed. Unfortunately, the heterogeneity of patients’ motor function capability in task space is not taken into account during the implementation of these controllers. In this paper, a new scheme called greedy AAN (GAAN) controller is designed for the upper limb rehabilitation training of neurologically impaired subjects. The proposed GAAN control paradigm includes a baseline controller and a Gaussian RBF network that is utilized to model the functional capability of subjects and to provide corresponding a task challenge for them. In order to avoid subjects’ slacking and encourage their active engagement, the weight vectors of RBF networks evaluating subjects’ impairment level are updated based on a greedy strategy that makes the networks progressively learn the maximum forces over time provided by subjects. Simultaneously, a challenge level modification algorithm is employed to adjust the task challenge according to the task performance of subjects. Experiments on 12 subjects with neurological impairment are conducted to validate the performance and feasibility of the GAAN controller. The results show that the proposed GAAN controller has significant potential to promote the subjects’ voluntary engagement during training exercises.