This paper presents the development of an exoskeleton glove system for people who suffer from brachial plexus injuries, aiming to assist their lost grasping functionality. The robotic system consists of a portable glove system and an embedded controller. The glove system consists of Linear Series Elastic Actuators (LSEA), Rotary Series Elastic Actuators (RSEA), and optimized finger linkages to provide imitated human motion to each finger and a coupled motion of the hand. The design principles and optimization strategies were investigated to balance functionality, portability, and stability. The model-based force control strategy compensated with a backlash model and model-free force control strategy are presented and compared. Results show that our proposed model-free control method achieves the goal of accurate force control. Finally, experiments were conducted with the prototype of the developed integrated exoskeleton glove system. Results from 3 subjects with 150 trials show that our proposed exoskeleton glove system has the potential to be used as a rehabilitation device for patients.