We conducted a dissipative particle dynamics simulation on the motion of polymer-grafted nanoparticles in entangled polymer melts. Three regimes for the mean square displacement of the nanoparticles were discovered at different time scales. The nanoparticles undergo Brownian diffusion at short and long time scales and exhibit subdiffusive behavior at intermediate time scales. The short-time diffusion can be approximated as the motion of bare nanoparticles, while the long-time diffusion is associated with the entire polymer-grafted nanoparticle. The long-time Brownian diffusion was found to be nonGaussian, which originates from the hopping diffusion of polymer-grafted nanoparticles in entangled polymer melts. The results nicely support the experimental findings and provide a comprehensive insight into the anomalous dynamics of polymer-grafted nanoparticles in polymer melts.