Minimizing weight and required motor torque as well as improving comfort is critical in designing exoskeletons. This paper proposes a novel non-circular gear-attached four-bar (NGF) mechanism with a J-shaped instantaneous center of rotation (ICR) for a knee exoskeleton. In this work, the ICR of the knee is classified into two distinct groups. One, is the physiological ICR, and the other is the ICR of the knee. These two ICRs were measured by fluoroscopy and motion capture of a healthy volunteer, respectively. Using a kinematic approach, the tracking error of both ICRs are minimized and the best-fitted elliptical curve for each of the ICRs is obtained. Next, the two elliptical curves are combined and a pair of non-circular gears is designed. Finally, system dynamics is considered to obtain design parameters resulting in minimum range of actuator torque while minimizing the mechanism weight.