The low frequency and broadband reduction of vibration and sound from damping treatment is one of the major concerns in research and engineering. In this paper, the combination of artificial metamaterial and damping design is used to improve the reduction effect. The vibration and sound radiation properties of the bare, free layered damping and metamaterial damping panels are compared and studied. Via the comparison of various panels, the vibration and sound radiation reduction and the enhancement from metamaterial damping are analysed. The effects of the material parameters of metamaterial damping elements are studied also. The numerical results indicate that the vibration reduction is significantly improved from the metamaterial damping in quite wide frequency ranges from low to high frequencies; the sound radiation is suppressed effectively also, especially the peaks are reduced obviously. A better reduction effect can be obtained via metamaterial design even with the same added mass as traditional damping treatment, especially, at the middle to low frequencies. The effects from the material parameters of metamaterial damping design are different from those of free layered damping design. And the manipulation and control of the damping effects from metamaterial design will be flexible and easy to realize. Further, an experimental system is built, and the experimental study and verification are carried out. The significant reduction and obvious enhancement from metamaterial damping design are observed from the experimental results.