A Long Term Evolution (LTE) eNodeB Medium Access Control (MAC) uplink scheduler is proposed in this paper for Single Carrier Frequency Division Multiple Access (SC-FDMA) as the uplink transmission scheme. Uplink scheduling algorithms available in literature commonly do not consider all the essential features of the LTE uplink. The proposed scheduler is shown to provide efficient allocation of radio resources to User Equipments (UEs) according to Quality of Service (QoS) of various traffic classes and the instantaneous channel conditions. The scheduler functionality is divided into Time Domain Packet Scheduling (TDPS) and Frequency Domain Packet Scheduling (FDPS). The proposed scheduler also supports multi-bearer UEs. The performance of the proposed scheduler is compared with common TDPS schedulers like Blind Equal Throughput (BET), Maximum Throughput (MT) and Proportional Fair (PF). The results show that the proposed scheduler guarantees provision of QoS to UEs and achieves an acceptable performance in terms of throughput.