Because of their ultra small, nanometer scale size and low density, the surface area to mass ratio (specific area) of carbon nanotubes (CNTs) is extremely large. Therefore, in a nanotube-based polymeric composite structure, it is anticipated that high damping can be achieved by taking advantage of the interfacial friction between the nanotubes and the polymer resin. In addition, the CNT’s large aspect ratio and high elastic modulus features allow for the design of such composites with large differences in strain between the constituents, which could further enhance the interfacial energy dissipation ability. Despite their wonderful engineering potential, the damping properties of CNT-based composites have not been examined in any detail. The purpose of this paper is to investigate the structural damping characteristics of polymeric composites containing single-walled carbon nanotubes (SWNTs), with a focus on analyzing the interfacial interaction between the CNT and the resin materials. The system is modeled using a four-phase composite, composed of a resin, voids, and bonded and debonded nanotubes. A micromechanical model is proposed to describe interfacial debonding evolution. To characterize the overall behavior, Weibull’s statistical function is employed to describe the varying probability of nanotube debonding under uniaxial loading. To address damping effects, the concept of interfacial “stick-slip” frictional motion between the nanotubes and the resin is proposed. The developed method is extended to analyze composites with randomly oriented nanotubes. The analytical results show that the critical shear stress, nanotube weight ratio and structure deformation are the factors affecting the damping characteristic. Experiments are also performed to verify the trends predicted by the analysis. Through comparing with neat resin specimens, the study shows that one can enhance damping by adding CNT fillers into polymeric resins. It is also observed that SWNT-based composites could achieve higher damping than composites with several other types (different size, surface area, density and stiffness) of fillers. These results confirm the possible advantage of using CNTs for damping enhancement.