In order to improve the numerical modeling of vertical turbulent transport of water vapor and sensible heat in atmospheric boundary layer and also the simulation of fog, this paper adopts the three-dimensional non-hydrostatic WRF model, with the help of a scale-aware MYNN_SA scheme of both local and non-local turbulences, to simulate a dense foggy weather process that occurred in a broad region from North China to Jiang-Huai Region during 28-29 December 2017. Impacts of the scale-aware boundary-layer turbulent scheme on the development of stable boundary layer, the turbulent transport and the simulation of fog are focused in a model resolution from mesoscale to large eddy. Compared with the surface observations in China and the ERA5 data, the scale-aware MYNN_SA scheme can improve the results of sub-grid-scale turbulent mixing when model resolution approaches the gray-zone scale, which shows better fog density, spatial and temporal variation of the dense fog in comparison with the original MYNN scheme. Detailed vertical structures of the fog, liquid cloud water and temperature inversion are well simulated by the scale-aware MYNN_SA scheme.