Non-orthogonal multiple access (NOMA) with power-domain user multiplexing has been considered as one of the potential candidates of the fifth-Generation (5G) systems. In this paper, a two-stage user selection algorithm is proposed based on proportional fairness for downlink NOMA with zero-forcing beamforming (PF-NOMA-ZFBF) in order to improve the throughput-fairness trade-off for NOMA system. We focus on short term fairness, where short term refers to the minimum time window in which a specified fairness is guaranteed and evaluated using Jain's index. A transmit power allocation then applied to enhance the throughput of NOMA system. Simulation results show that the proposed PF-NOMA-ZFBF significantly improves user fairness index with at least 38.96% over conventional NOMA-ZFBF while maintaining the total system sum-rate (near maximum).