The human knee joint exhibits complex motion characterized by a varying instantaneous center of rotation. Mimicking this motion in mechanical systems holds significant potential for both scientific understanding and engineering design. To this end, this study investigates a design method of the biomimetic robot joint (BRJ) inspired by the human knee, aiming to accurately reproduce its motion. Firstly, the bionic concept and the design of the BRJ mechanism with one degree of freedom are introduced. The proposed mechanism incorporates a higher pair composed of three pairs of line-curve contact elements, each maintaining mutual contact and all remaining simultaneously engaged to ensure continuous and stable joint motion. Then, the profile synthesis method is presented to determine the geometry of elements forming the higher pair. Next, the kinematic model of the BRJ mechanism is developed. Finally, a case study is conducted to validate the effectiveness of the proposed design. Results indicate that the BRJ mechanism can accurately reproduce the desired complex motion with one degree of freedom, offering a novel joint solution for applications such as exoskeletons, prostheses, and rehabilitation robots.