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In this paper, we propose a novel non-orthogonal multiple access (NOMA) scheme with beamwidth control for hybrid millimeter wave communication systems and study the resource allocation design to maximize the system energy efficiency. In particular, NOMA transmission allows more than one user to share a single radio frequency chain, which is beneficial to enhance the system energy efficiency. More importantly, the proposed beamwidth control can increase the number of served NOMA groups by widening the beamwidth that can further exploit the energy efficiency gain brought by NOMA. To this end, two beamwidth control methods, based on the conventional beamforming and the Dolph–Chebyshev beamforming, respectively, are proposed. We first characterize the main lobe power losses due to the two beamwidth control methods and propose an effective analog beamformer design to minimize the power loss. Then, we formulate the energy-efficient resource allocation design as a non-convex optimization problem, which takes into account the minimum required user data rate. A NOMA user grouping algorithm based on the coalition formation game theory is developed and a low-complexity iterative digital precoder design is proposed to achieve a locally optimal solution utilizing the quadratic transformation. Simulation results verify the fast convergence and effectiveness of our proposed algorithms. In addition, our results demonstrate the superior energy efficiency achieved by our proposed beamwidth controlling NOMA scheme compared to the conventional orthogonal multiple access and NOMA schemes without beamwidth control.