To compensate for the adverse effects caused by radio link in worldwide interoperability for Microwave Access (WiMAX) networks, many radio resource management approaches have been present to assign orthogonal frequency division multiplexing access slots for seeking better performance. However, no WiMAX standards for optimal slot allocation have been defined. In this study, a new uplink bandwidth allocation scheme, GRAMA, which combines grey relational analysis with multiple attributes and the knapsack algorithms, is proposed to improve resource utilization while satisfying the user's requirements of throughput and fairness. Channel aware technology and service flow priority are used in the proposed scheme to achieve the highest performance index. A series of simulation is conducted under the scenarios of constant-bit-rate (CBR) voice traffic, variable-bit-rate (VBR) video traffic, and VBR data traffic. The performance is evaluated in terms of bandwidth utilization, transmission throughput, and fairness and simulation result which indicate that the proposed GRAMKA outperforms the conventional fuzzy and knapsack algorithms.