The radio resource allocation is one of the most important issues to achieve effective wireless communication. In Long Term Evolution (LTE) network, single carrier frequency division multiple access (SC-FDMA) is applied as the transmission technology for uplink traffic. Most researches focus on maximizing the system throughput of SC-FDMA under changeable channel condition. However, users may require different quality of services (QoS) for different applications. This paper studies radio resource allocation for QoS users in localized SC-FDMA system. The proposed scheme divides allocation process into matching algorithm and radio resource assignment algorithm. The Gale-Shapley algorithm is applied to find the optimal matching between resource blocks (RB) and user equipment (UE) by considering channel conditions and the desired QoS. Then the resource assignment algorithm heuristically allocates bandwidth to UE by referring the matched RB under the constraint of carrier continuity. This paper modified the Recursive Maximum Expansion (RME) algorithm to effectively assign radio resource for UEs with different bandwidth demands. The performance of our proposed scheme is compared with the modified RME scheme through exhaustive simulations. The video streaming, VoIP, and FTP traffic types were adopted for simulations. Our simulation results show that the proposed scheme achieves better QoS satisfaction and system throughput than the RME-modified scheme.