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For a multi-user orthogonal frequency division multiplexing (OFDM) system, system reliability, availability and fairness should be guaranteed simultaneously. Resource allocation problem for such systems can be described as maximizing overall throughput while satisfying requirement of fairness, subject to power restriction and quality of service (QoS) requirement. Existing researches provide solution with high throughput, but perform normally in fairness. Aiming at the problem, an adaptive resource allocation method is proposed. Firstly, sub-carriers are allocated equally to all users. Second, bits and power are loaded on the sub-carriers following Greedy algorithm for all users. Third, fairness is improved through joint adjustment to the sub-carriers, bits, and power. Simulations under typical urban channel were carried out, and results show that the proposed method can obtain nice BER performance and high throughput. What's more, it brings excellent fairness over the other methods. It is recommended to be adopted for services with tight fairness requirement.