The work aims to reduce the effect of wheel-footed packaging handling robot on working performance under the vibration impact during storage and transportation and meet the demand for vibration damping at the junction of wheel and leg. A design scheme that combined a hydraulic buffer and a mechanical damping device was proposed. The energy method and the finite element method were used to analyze stiffness coefficients of main elastic elements in the damping device. The stiffness characteristics of drive wheel under condition of different elastic elements were compared. A drive wheel combining the hydraulic buffer and the S-shaped elastic sheet was designed for the wheel-footed packaging handling robot. Then, the wheel movement experiment and environmental impact experiment of the prototype were carried out. During the experiments, the robot fluctuated very little in motion amplitude and ran smoothly, which indicated that the damping device of wheel-footed packaging handling robot could effectively reduce dropping impact, and lower physical impact of environment on the packaging. Thus, the rationality and practicability of the damping device were verified. The design scheme of damping device can effectively reduce the vibration impact of the wheel-footed packaging handling robot during working process and lower the physical effect of environment on packaging and can also improve the safety of the mechanical body and electrical components, thus making working performance more stable.