It has long been known that the radial density profiles of globular cluster systems (GCSs) in elliptical galaxies vary with the total luminosities of their host galaxies. In order to elucidate the origin of this structural non-homology in GCSs, we numerically investigate the structural properties of GCSs in elliptical galaxies formed from a sequence of major dissipationless galaxy merging. We find that the radial density profiles of GCSs in elliptical galaxies become progressively flatter as the galaxies experience more major merger events. The density profiles of GCSs in ellipticals are well described as power-laws with slopes (αgc) ranging from −2.0 to −1.0. They are flatter than, and linearly proportional to, the slopes (αs) of the stellar density profiles of their host galaxies. We also find that the GCS core radii (rc) of the density profiles are larger in ellipticals that experienced more mergers. By applying a reasonable scaling relation between luminosities and sizes of galaxies to the simulation results, we show that αgc ≈ −0.36MV − 9.2, rc ≈ −1.85MV, and αgc ≈ 0.93αs, where MV is the total V-band absolute magnitude of a galaxy. We compare these predictions with observations and discuss their physical meaning. We suggest that the origin of structural non-homology of GCSs in ellipticals can be understood in terms of the growth of ellipticals via major dissipationless galaxy merging.