Better simulation of the advection and distribution of moisture is highly significant for the improvement of numerical weather predictions, especially for precipitation. The computation of the advection process in a semi-Lagrangian model requires high accuracy, conservation of mass, positive and preserves the shape or spatial distribution of the advection quantity. However, the Quasi-Monotone Semi-Lagrangian (QMSL) scheme adopted in the Global-Regional Assimilation and PrEdiction System, Global Forecast System (GRAPES_GFS) suffers from lower accuracy in the strong gradient and discontinuity region of the scalar field and cannot strictly conserve the mass. This study draws on research progress in computational fluid dynamics; it introduces a material advection scheme, the Piecewise Rational Method (PRM), which is based on a piecewise continuous rational function, into the GRAPES_GFS, solves the flux form of the water vapor equation, and treats the polar regions with a mixing technique. The two advection schemes were compared in a series of stand-alone and in-model ideal tests. The results proved that the PRM scheme is more precise than the QMSL scheme; in particular, in the area of large water vapor gradient, the dispersion and dissipation error is smaller, and the conservation and shape preservation are also better. An examination of batch prediction experiments in the GRAPES_GFS verified that the PRM scheme can effectively improve the simulation of the advection and distribution of moisture, improve the accuracy of precipitation forecasts, and also play a significant role in enhancing the comprehensive model performance.