The vibration and impact of a humanoid bipedal robot during movements such as walking, running and jumping may cause potential damage to the robot's mechanical joints and electrical systems. In this paper, a composite bidirectional vibration isolator based on magnetorheological elastomer (MRE) is designed for the cushioning and damping of a humanoid bipedal robot under foot contact forces. In addition, the vibration isolation performance of the vibration isolator was tested experimentally, and then, a vibration isolator dynamics model was developed. For the bipedal robot foot impact, based on the vibration isolator model, three vibration reduction control algorithms are simulated, and the results show that the vibration damping effect can reach 85%. Finally, the MRE vibration isolator hardware-in-the-loop-simulation experiment platform based on dSPACE has been built to verify the vibration reduction control effect of the fuzzy PID algorithm. The result shows the vibration amplitude attenuates significantly, and this verifies the effectiveness of the fuzzy PID damping control algorithm.