Due to the power consumption issue of user equipment (UE), Single-Carrier FDMA (SC-FDMA) has been selected as the uplink multiple access scheme of 3GPP Long Term Evolution (LTE). Similar to OFDMA downlink, SC-FDMA enables multiple UEs to be served simultaneously in uplink as well. However, the single carrier characteristic requires that all the allocated subcarriers to a UE must be contiguous in frequency with each time slot. Moreover, a UE should adopt the same modulation and coding scheme at all allocated subcarriers. These two constraints do limit the scheduling flexibility. In this paper, we formulate the UL scheduling problem with proportional fairness support by taking two constraints into consideration. Since this optimization had been proven to be an NP-hard problem, we further develop one heuristic algorithm. We demonstrate that competitive performance can be achieved in terms of system throughput, which is evaluated by using 3GPP LTE system model simulations.