Abstract: In a series of papers, for the semi-implicit semi-Lagrangian GRAPES model, the highaccuracy and positivedefinite advection scheme called the piecewise rational function methed (PRM) is developed. First, in Part I of the papers, it was found that this scheme is simple, practical and easy to code and has great ability in treating the variables of large spatial variation. Its feasibility in the GRAPES can also be confirmed by ideal experiments. In Part Ⅱ, the 24 hour rainfall forecast has been made continuously for one month: July in 2005. Through detailed case analyses based on a comparison of the monthly mean 24 hour rainfall and the calculation of TS (Threat Score), it is found that the spatial distribution of forecasted rainbelts by the PRM is similar to that by the original water substances advection scheme utilized in GRAPES model but the PRM shows obvious advantages over the latter in forecasting the rainfall larger than 25 mm/day both for the rainfall amount and occurring location of heavy rainfall and, is more sensitive to the grid scale precipitation. As a result, the highorder accuracy and positivedefinite advection scheme can improve the forecast. Particularly, this scheme has great potentialities to improve the heavy rainfall forecast. The PRM advection scheme is more rational to calculate water substance distribution than the original QMSL. Especially, it also has ability in describing the large horizontal gradient of lower atmosphere moisture field over the East Asian region during the Meiyu season as well as the case of larger small scale variability along the Meiyu front.