A molecular model of silica nanoparticles grafted with poly(ethylene oxide) oligomers has been developed for predicting the transport properties of nanoparticle organic-hybrid materials (NOHMs). Ungrafted silica nanoparticles in a medium of poly(ethylene oxide) oligomers were also simulated to clarify the effect of grafting on the dynamics of nanoparticles and chains. The model approximates nanoparticles as solid spheres and uses a united-atom representation for chains, including torsional and bond-bending interactions. The calculated viscosities from Green-Kubo relationships and temperature extrapolation are of the same order of magnitude as experimental data but show a smaller activation energy relative to real NOHMs systems. Grafted systems have higher viscosities, smaller diffusion coefficients, and slower chain dynamics than the ungrafted ones at high temperatures. At lower temperatures, grafted systems exhibit faster dynamics for both nanoparticles and chains relative to ungrafted systems, because of lower aggregation of particles and enhanced correlations between nanoparticles and chains. This agrees with the experimental observation that NOHMs have liquidlike behavior in the absence of a solvent. For both grafted and ungrafted systems at low temperatures, increasing chain length reduces the volume fraction of nanoparticles and accelerates the dynamics. However, at high temperatures, longer chains slow down nanoparticle diffusion. From the Stokes Einstein relationship, it was determined that the coarse-grained treatment of nanoparticles leads to slip on the nanoparticle surfaces. Grafted systems obey the Stokes-Einstein relationship over the temperature range simulated, but ungrafted systems display deviations from it.