Using a cosmological dark matter simulation of a galaxy-cluster halo, we follow the temporal evolution of its globular cluster population. To mimic the red and blue globular cluster populations, we select at high redshift (z ∼ 1) two sets of particles from individual galactic halos constrained by the fact that, at redshift z = 0, they have density profiles similar to observed ones. At redshift z = 0, approximately 60% of our selected globular clusters were removed from their original halos building up the intra-cluster globular cluster population, while the remaining 40% are still gravitationally bound to their original galactic halos. Since the blue population is more extended than the red one, the intra-cluster globular cluster population is dominated by blue globular clusters, with a relative fraction that grows from 60% at redshift z = 0 up to 83% for redshift z ∼ 2. In agreement with observational results for the Virgo galaxy cluster, the blue intra-cluster globular cluster population is more spatially extended than the red one, pointing to a tidally disrupted origin.