Long Term Evolution (LTE) is a promising technology for 4G mobile networks. Due to utilize OFDMA in downlink and SC-FDMA in uplink, the LTE system is expected to provide significantly high throughput with 20 MHz spectrum allocation. To increase the cell throughput and multi-user diversity gain, channel dependent scheduling (CDS) is implemented for the OFDMA-based multi-user scenario to allocate resource blocks (RBs) to users experiencing better channel conditions. Nevertheless, CDS may not perform well in SC-FDMA due to its two inherent constraints one is contiguous RB assignment and the other is robust modulation and coding mode. In this paper, the formulation of resource allocation for a SC-FDMA system upon considering two inherent constraints is proposed. Since the optimization problem of resource allocation in SC-FDMA is NP-hard, we further propose two heuristic algorithms to find feasible solutions. We evaluate the proposed formulation and heuristic algorithms by conducting simulation. The simulation results show that our methods achieve significant performance improvement not only in system sum throughput but also in transmission delay.