With the development of society, aging population and the number of stroke patients is increasing year by year. Rehabilitation exoskeleton can help patients to carry out rehabilitation training and improve their activities of daily living (ADL). First of all, a reconfigurable exoskeleton for upper limb rehabilitation is designed in this paper. The exoskeleton combines gravity compensation with left-right arm switching function through its reconfigurability. Secondly, the motion space and singular configuration of the exoskeleton are analyzed. By changing the working mode of the gravity compensation device, the control experiment of the motor is carried out. The influence of gravity compensation device on motor driving torque and energy consumption is analyzed. Finally, the results of experiment show that, in the best case, the gravity compensation device can reduce the energy consumption by 41.15% and the maximum motor current by 33.56% of the driving element.