The dynamic channel allocation (DCA) scheme in multi-cell systems causes serious inter-cell interference (ICI) problem to some existing calls when channels for new calls are allocated. Such a problem can be addressed by advanced centralized DCA design that is able to minimize ICI. Thus, in this paper, a centralized DCA is developed for the downlink of multi-cell orthogonal frequency division multiple access (OFDMA) systems with full spectral reuse. However, in practice, as the search space of channel assignment for centralized DCA scheme in multi-cell systems grows exponentially with the increase of the number of required calls, channels, and cells, it becomes an NP-hard problem and is currently too complicated to find an optimum channel allocation. In this paper, we propose an ant colony optimization (ACO) based DCA scheme using a low-complexity ACO algorithm which is a kind of heuristic algorithm in order to solve the aforementioned problem. Simulation results demonstrate significant performance improvements compared to the existing schemes in terms of the grade of service (GoS) performance and the forced termination probability of existing calls without degrading the system performance of the average throughput.