We have carried out molecular dynamics simulations of model polymer-nanoparticle composites (PNCs) consisting of coarse-grained bead-necklace polymer chains and roughly spherical nanoparticles comprised of like beads for the purpose of gaining understanding of the influence of the nanoparticle-polymer interface on the viscoelastic properties of PNCs. The dynamic shear modulus G(c)(t) and viscosity eta(c) of the PNCs were determined as a function of nanoparticle volume fraction, specific nanoparticle-polymer interfacial area, and the nature of the nanoparticle-polymer interaction. The viscoelastic properties of the PNCs were well described as a product of a polymer matrix dynamic shear modulus or viscosity and a particle volume fraction dependent effect independent of particle size, analogous to treatments of conventional particle composites. In contrast to many conventional composites, however, the viscoelastic properties of the polymer matrix were strongly perturbed by the nanoparticles and depended upon the nature of the nanoparticle-polymer interactions.