In this paper, an adaptive knee joint orthosis with a variable rotation center for biomimetic motion rehabilitation assistance suitable for patients with knee joint movement dysfunction is designed. Based on the kinematic information of knee joint motion obtained by a motion capture system, a Revolute-Prismatic-Revolute (RPR) model is established to simulate the biomimetic motion of the knee joint, then a corresponding implementation for repetitively driving the flexion-extension motion of the knee joint, mainly assembled by a double-cam meshing mechanism, is designed. The pitch curve of each cam is calculated based on the screw theory. During the design process, size optimization is used to reduce the weight of the equipment, resulting in a reduction from 1.96 kg to 1.16 kg, achieving the goal of lightweight equipment. Finally, a prototype of the designed orthosis with the desired biomimetic rotation function is prepared and verified. The result shows that the rotation center of the prototype can achieve biomimetic motion coincident with the rotation center of an active knee joint, which can successfully provide rehabilitation assistance for the knee joint flexion-extension motion.