Single carrier frequency division multiple access (SC-FDMA) is applied as the transmission technology for the uplink traffic in LTE networks. The radio resource allocation is one of the most important issues to achieve effective wireless communication. Most researches focus on maximizing the system throughput of SC-FDMA under changing channel condition. However, users may require different quality of services (QoS) for different applications. This paper studies the radio resource allocation for QoS users in using localized SC-FDMA transmission. The proposed scheme is divided into the matching algorithm and the radio resource assignment algorithm. The Gale-Shapley algorithm is applied to find the optimal matching of resource block (RB) by considering the channel condition and the desired QoS of UE. The Recursive Maximum Expansion (RME) algorithm is modified in this paper to effectively assign radio resource for UEs with different bandwidth demands. The video streaming, VoIP, and FTP traffic types were adopted for simulations. Our results show that the proposed scheme achieves better QoS satisfaction than that without matching mechanism.