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An efficient fairness-aware uplink resource allocation algorithm in orthogonal frequency-division multiplexing-based cognitive radio systems is presented. The proposed resource allocation algorithm is divided into two steps. The subcarriers to user assignment is first performed, and then the power is allocated to the different subcarriers. The objective is to maximise the total data rate while guaranteeing that the interference introduced to the primary system is under the prescribed interference temperature limit. The fairness among users is considered within the subcarrier allocation by reducing the probability of having users whose instantaneous rates are below a given minimum rate. Many factors will be considered during the resource allocation process like the channel quality, potential interference caused to the primary bands, instantaneous rate achieved by every user and the increment in the total data rate. Simulation results confirm the efficiency of the proposed algorithm.