Supernumerary robotic limbs (SRLs) are novel wearable assistive devices that can expand the workspace of the wearer. Benefiting from the excellent compliance, adaptability to complex environments, and human-robot interaction of pneumatic-actuated robots, researchers have integrated pneumatic actuators with robotic limbs to create flexible SRL. However, existing pneumatic SRL commonly suffer from low load capacity and control difficulties. In response to these phenomena, this study draws inspiration from the flexible and controllable characteristics of multi-joint movements and muscle stiffness in vertebrates, a pneumatic-tendon hybrid-actuated SRL is designed, consisting of multiple fiber-reinforced actuators (FRAs), tendons and rigid support structure, the FRA is used to simulate the muscle tissue of vertebrates to achieve variable stiffness. The rigid support structure mimics the biological internal skeleton to ensure structural stability and reliability. The tendon-actuated structure simulates the ligament tissue connecting the internal skeleton to achieve precise and controllable motion. This design addresses the prevalent issues of low load capacity and motion control challenges in current pneumatic SRLs. The kinematic model of the pneumatic-tendon hybrid-actuated SRL is analyzed, and the mechanism of FRA motion under pressurized air is parameterized. Experiments are conducted to validate the proposed robot.