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Orthogonal Frequency Division Multiple Access (OFDMA) based cellular network can support diverse requirement of multimedia traffic. OFDMA method using adaptive modulation and coding technique can increase the system capacity many fold. In order to meet dynamic bandwidth requirement in downlink, an efficient resource allocation method called Two Stage Rate Adaptive (TSRA) algorithm is proposed here. The TSRA employs an adaptive modulation techniques and a Band Width Adaptation (BWA) algorithm to support the dynamic resource requirement of a multimedia traffic. The BWA is invoked dynamically by TSRA to deal with real-time variable bit rate services. It is observe that the simulated average system capacity exceeds 6 b/s per Hz, and approaches analytical/theoretical limit for increasing no of users. The delay performance is observed for existing and new arrival of multimedia traffic. We also simulate the average BER performance of the TSRA algorithm.