Mechanism parameters of bipedal robots are crucial for achieving efficient locomotion in complex environments. Inspired by the human energy-efficient walking style, this paper proposes a novel concept of full-range walking energy efficiency and explores the optimal linkage mechanism within certain ranges of step length and walking speed for bipedal robots. First, a bipedal model incorporating an upper body is established for dynamic analysis. Next, an optimal walking gait subject to walking constraints is solved by considering the full-range energy efficiency. Further, an optimal linkage mechanism is investigated, and the influence of dynamic parameters on energy efficiency is analyzed. Finally, the push-off impulse, minimum ground support force, and walking torque features are discussed. It shows that the full-range walking energy efficiency can be lowered by reducing the ratio of leg mass, concentrating mass at the hip joint, decreasing the length of the upper body, or increasing the center of mass of the leg. In addition, efficient walking motion can be achieved by designing the coordination of positive hip joint torque and push-off impulse at the ankle. This paper can be used to guide the mechanism parameter optimization and efficient walking gait design of bipedal robots.