A nonequilibrium molecular dynamics model combined with quantum correction is presented for characterizing the thermal conductivity of graphene nanoribbons (GNR). Temperature effect on graphene nanoribbon thermal conductivity is revealed based on this model. It is shown that different from the decreasing dependence in classical nonequilibrium molecular dynamics simulations, an “anomaly” is revealed at low temperatures using quantum correction. Besides, the conductivity of GNR shows obvious edge and scale effects: The zigzag GNR have higher thermal conductivity than the zigzag GNR. The whole temperature range of thermal conductivity and the slope of thermal conductivity at low temperatures both show an increasing dependence of width. Boltzmann-Peierls phonon transport equation is used to explain the temperature and scale effects at low temperatures, indicating that the model constructed is suitable for a wide temperature range of accurate calculation for thermal conductivity of different chirality and width. Research provides a possible theoretical and computational basis for heat transfer and dissipation applications of GNR.