Using a cosmological N-body numerical simulation of the formation of a galaxy cluster- sized halo, we analyze the temporal evolution of its globular cluster population. We follow the dynamical evolution of 38 galactic dark matter halos orbiting in a galaxy cluster that at redshift z=0 has a virial mass of 1.71 * 10 ^14 Msol h^-1. In order to mimic both "blue" and "red" populations of globular clusters, for each galactic halo we select two different sets of particles at high redshift (z ~ 1), constrained by the condition that, at redshift z=0, their average radial density profiles are similar to the observed profiles. As expected, the general galaxy cluster tidal field removes a significant fraction of the globular cluster populations to feed the intracluster population. On average, halos lost approximately 16% and 29% of their initial red and blue globular cluster populations, respectively. Our results suggest that these fractions strongly depend on the orbital trajectory of the galactic halo, specifically on the number of orbits and on the minimum pericentric distance to the galaxy cluster center that the halo has had. At a given time, these fractions also depend on the current clustercentric distance, just as observations show that the specific frequencyof globular clusters S_N depends on their clustercentric distance. ; Comment: 11 pages, 8 figures. Accepted for publication in ApJ