This paper proposes an efficient downlink resource allocation scheme for Orthogonal Frequency Division Multiple Access based WiMAX systems using the Adaptive Modulation and Coding mode operation. Given a set of user requests, the proposed algorithm determines the modulation scheme and allocates a two-dimensional (time and frequency) burst to each user. It is known that finding the optimal solution for such a resource allocation problem is NP-complete. To reduce the computation complexity, this paper proposes a heuristic solution. Compared with the Efficient Downlink Bandwidth Allocation (EDBA) algorithm [6], the proposed scheme achieves higher channel utilization and system throughput with similar execution time. Simulation results show that the average channel utilization of the proposed scheme is about 75~85% and that of EDBA is about 60~70%.