To address the issues of non-standard rehabilitation processes among upper-limb hemiplegic patients caused by cerebrovascular-accident (CVA) and the shortage of rehabilitation physicians, a 5-degree-of-freedom (DOF) upper-limb elbow-wrist joint rehabilitation robot and its control system was proposed, aiming to better meet the flexible rehabilitation needs of patients. The rehabilitation robot platform is a 3-RRR serial mechanism, which can achieve independent elbow joint flexion-extension rehabilitation, independent wrist joint flexion-extension and internal-external rotation rehabilitation, coordinated elbow-wrist joint flexion-extension rehabilitation, and coordinated elbow joint flexion-extension and wrist joint internal-external rotation rehabilitation. Also, considering the different hemiplegic sides of patients, the rehabilitation robot was equipped with a mirror function. The touch screen communicates with the planar-lightwave circuit (PLC) to enable human-machine interaction. Matlab software was used to draw the workspace cloud map of the robot by the Monte-Carlo (M-C) method, so as to carry out more effective task planning and operation control. The results show that the developed prototype can meet the movement rehabilitation of the upper-limb elbow-wrist joint in multiple modes and can train both the flexor and extensor muscle groups.