This paper investigates the application of nonorthogonal multiple access (NOMA) in millimeter wave (mmWave) communication with beamforming, user selection and power allocation. To overcome the burden of feedback, random beamforming to mmWave NOMA systems is considered. We then formulate an optimization problem to maximize the sum rate of the proposed mmWave NOMA systems, which is nonconvex. To solve the challenging problem, we invoke the branch and bound (BB) technique to develop an optimal power allocation algorithm. Then a low complexity suboptimal algorithm based on matching theory is proposed to realize user selection. Simulation results are provided for validating the effectiveness of the proposed algorithms and to show that the sum rate performance of the mmWave NOMA systems can be substantially improved by the proposed algorithms compared to the conventional mmWave orthogonal multiple access (OMA) systems.