Single-carrier frequency division multiple access (SC-FDMA), which is similar to multi carrier modulation type with orthogonal frequency domain multiple access (OFDMA), has been used as long term evolution (LTE) uplink access method due to its low PAPR and high UE power efficiency. SC-FDMA, however, has a constraint that subcarriers must be consecutively allocated to each user for every time slot due to the single carrier feature of the access type. This paper proposes an LTE uplink scheduling algorithm satisfying the contiguity constraint of resource allocation and ensuring high cell (system) throughput and fairness with low complexity. The proposed scheme, named MSCC, preferentially considers allocation to RBs based on the highest Proportional Fair scheduling metric in each physical resource block (RB) with the contiguity constraint. As a result of simulation analysis, MSCC has better fairness and cell throughput than the previous schemes (i.e., RME, IRME algorithm) by 10% and 17% at most, respectively. We also analyze cell edge user throughput (the gathering with the cell users who have 5% lowest throughput) and PAPR. In the appendix, complexity analysis shows that the time complexity of the MSCC is better than the previous schemes.