Using the most advanced anisotropic (2D) Fokker-Planck (FP) models, we calculate the evolution of the mass functions of the Galactic globular cluster system (GCMF). Our models include two-body relaxation, binary heating, tidal shocks, dynamical friction, stellar evolution, and realistic cluster orbits. We perform 2D-FP simulations for a large number of virtual globular clusters and synthesize these results to study the relation between the initial and present GCMFs. We found two probable IGCMFs that eventually evolve into the Milky Way GCMF : truncated power-law, and log-normal model with higher initial low mass limit and peak mass than the earlier studies.