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This paper presents an adaptive sub-carrier and power allocation scheme for orthogonal frequency division multiple access (OFDMA) systems according to their different quality of service (QoS) requirements and traffic type. The algorithm maximized the transmission data rate while satisfying total power constraint and a certain bit error rate (BER) requirement. A greedy algorithm known to be the most efficient algorithm for this problem can provide a high quality optimal solution, but has the disadvantage of incurring a long computation time. This problem should be solved in a real-time environment. The proposed algorithm not only avoids the high complexity but also provides considerable universality and flexibility for both the fixed rate voice data and variable rate multimedia data of the broadband wireless communication. It mainly consists of two steps. The first is the allocation of sub-carriers and power alternately to the real-time user. The second is the residual resource distribution to the non-real-time users. The simulation results demonstrate that the scheme has computational advantages over the conventional algorithms while providing the QoS guarantee.