In this paper, the damping characteristics of epoxy resin containing aligned or randomly oriented carbon nanotube (CNT) ropes are investigated via a multiscale analysis approach. The shear strengths at the inter-tube and tube-resin interfaces are calculated using molecular dynamics simulations of nanotube pullouts before being applied to a micromechanical damping model. In the micromechanical model, the composite is described as a three-phase system composed of a resin, a resin sheath acting as a shear transfer zone, and a carbon nanotube rope. The concept of stick-slip motion is used to describe the load transfer behavior between carbon nanotubes in a rope as well as between nanotubes and the surrounding sheath. Both the energy dissipations from the viscoelastic polymer matrix and from the stick-slip motion are included in the overall structural damping characteristics. The effect of nanorope alignment on damping characteristics is also presented.