In this paper, a position-aided beam training (PBT) in millimeter wave (mmWave) non-orthogonal multiple access (NOMA) systems method is proposed. Position information can be used to compute the angle of beam pointing and essentially eliminate the beam alignment overhead. Based on the angle, a clustering method based on k-means is conducted to cluster users. After clustering, the beamforming method based on the cluster center is developed to reduces interference between each cluster. Finally, power allocation for downlink NOMA is put forward to maximize sum rate with user position information. Simulation analysis confirm the superiority of the proposed method over the conventional ones in performance.