In this paper, we propose an energy-efficient robotic leg design using a redundantly actuated parallel mechanism (RAPM). By adding an actuator parallel to the serially-actuated leg, we show that the legged machine can reduce mechanical energy loss. We begin with reviewing kinematic model of parallel mechanisms and then present an optimal torque distribution algorithm among redundant actuators which minimizes antagonistic power, a measure for mechanical energy loss due to power conflict in actuators. As an example study, given end-effector (foot) force and motion profile generated by the spring-loaded-inverted-pendulum (SLIP) running, we demonstrate how much the antagonistic power can be reduced by applying the proposed leg design and optimization algorithm in simulation. Also, it is presented that the choice of actuated joints in parallel mechanism affects the performance (energy efficiency). Finally, we demonstrate that the proposed design is also effective in walking, which validates the hypothesis that the proposed RAPM leg design can be effective in a range of locomotion tasks.