We study the dynamical evolution of the M87 globular cluster (GC) system using the most advanced and realistic Fokker-Planck (FP) model.By comparing our FP models with both mass function (MF) and radial distribution (RD) of the observed GC system, we find the best-fit initial (at M87's age of 2-3 Gyr) MF and RD for three GC groups: all GCs, blue GCs, and red GCs. We estimate the initial total mass in GCs to be 1.8+0.3-0.2 X 1010⊙, which is about 100 times larger than that of the Milky Way GC system. We also find that the fraction of the total mass currently in GCs is 34%. When blue and red GCs are fitted separately, blue GCs initially have a larger total mass and a shallower radial distribution than red GCs. If one assumes that most of the significant major merger events of M87 have ended by the age of 2-3 Gyr, our finding that blue (metal-poor) GCs initially had a shallower radial distribution supports the major merger scenario for the origin of metallicity bimodality.