Unlike the initial mass function, the initial size distribution of globular cluster (GC) systems is not well known. We calculate the evolution of the mass function (MF), radial distribution (RD), and size distribution (SD) of the Galactic GC system. By comparing the results from this calculation and the present-day MF, RD, and SD of the Galactic GC system, we infer the initial SD of the GC system. We find that a Gaussian distribution of the half-mass radius and a Gaussian distribution of the half-mass to Jacobi radius ratio are the best-fit initial SDs of the Galactic GC system.