In order to assist the patients without the hand movement function to grasp the daily necessities, a soft exoskeleton robot system based on wire tension feedback is developed, which can realize the stable control of the fingertip force. Firstly, the structural design and control strategy of the soft exoskeleton glove are introduced. Then a static mechanics model of the finger is established, and the contact force between the fingertip and the object is calculated by the wire tension at the entrance of the Bowden-cable. For the friction loss problem in Bowden-cable transmission, the variation range of the sum of the cumulative angles of the Bowden-cable paths is limited to the range of 0°~ 90° by the physical method. The friction compensation is performed by the method of median compensation. Finally, the grasping force control experiment of the soft exoskeleton glove proves the effectiveness of the static mechanics model of the finger and the friction compensation method. The maximum range of the fingertip force error is within ±1 N. A grasping experiment is performed on the patient without the hand movement function to verify the actual application effect of the soft exoskeleton glove. The experimental results show that the soft exoskeleton glove can assist patients to reliably grasp daily necessities.