In this paper, the influence of carbon nanotube functionalization on interfacial shear strength and hence on damping characteristics of CNT-based polymeric composites is investigated with a multiscale model. The sequential multiscale approach consists of two parts. First, the interfacial shear strength between the functionalized nanotube and the polymer is calculated by simulating a CNT pull-out test using the molecular dynamics method. The strength values obtained from atomic simulation are then applied to a micromechanical damping model of a representative unit cell of a CNT/polymer composite under cyclic loading. The analysis results indicate that the nanotube functionalization increases the interfacial shear strength. The increased shear strength can either enhance or reduce the effective loss factor of the composite, depending on the operational stress range.