This letter focuses on uplink transmission in OFDMA systems. A subcarrier and power allocation problem is formulated that maximizes the throughput of OFDMA uplink systems while satisfying each user's power constraints. A greedy algorithm known to be the most efficient algorithm for this problem can provide a high quality near-optimal solution, but has the disadvantage of incurring a long computation time. As this problem should be solved in a real-time environment, computation time is a very important performance measure of algorithms. In this letter, a computationally efficient algorithm that provides a nearly identical quality, near-optimal solution as the greedy algorithm but requires less than 10% of the computation time of the greedy algorithm is proposed.