Lower limb rehabilitation robots based on linkage-based mechanisms have recently drawn significant attention in the field due to their numerous advantages. The control of previously proposed linkage-based gait rehabilitation robotic orthoses has been achieved using constant speed control without consideration for the interaction forces. However, such an approach can be harmful to people with stroke since the level of disability varies among individuals, and it may cause potential injuries when excessive force is applied by the robot. To overcome this limitation and improve the rehabilitation process, it is necessary to recognize the force exerted by the person during walking and adjust the robot’s assistive torque accordingly, to provide synchronized motion. Thus, in this work, a human-cooperative approach based on a stiffness control strategy for the six-bar linkage-based gait rehabilitation robot is presented. The proposed methodology can serve as a solid foundation for developing a human-cooperative approach for linkage-based lower limb rehabilitation robotic orthoses. The control was validated and tested with eight healthy human subjects. As a result, customized robotic assistance with this mechanism can be provided during training to meet the individual needs of stroke patients, which can lead to increased engagement and contribution, thus improving treatment outcomes.