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Full-duplex (FD) millimeter-wave (mmWave) multiple-input multiple-output (MIMO) communication is a promising solution for the extremely high-throughput requirements in future cellular systems. The hybrid beamforming structure is preferable for its low hardware complexity and low power consumption with acceptable performance. In this paper, we introduce the hardware efficient dynamic subarrays to the FD mmWave MIMO systems and propose an effective hybrid beamforming design to cancel the self-interference (SI) in the considered system. First, assuming no SI, we obtain the optimal fully digital beamformers and combiners via the singular value decomposition of the uplink and downlink channels and the water-filling power allocation. Then, based on the obtained fully digital solutions, we get the dynamic analog solutions and digital solutions using the Kuhn–Munkres algorithm-aided dynamic hybrid beamforming design. Finally, we resort to the null space projection method to cancel the SI by projecting the obtained digital beamformer at the base station onto the null space of the equivalent SI channel. We further analyze the computational complexity of the proposed method. Numerical results demonstrate the superiority of the FD mmWave MIMO systems with the dynamic subarrays using the proposed method compared to the systems with the fixed subarrays and the half-duplex mmWave communications. When the number of RF chains is 6 and the signal-to-noise ratio is 10 dB, the proposed design outperforms the FD mmWave MIMO systems with fixed subarrays and the half-duplex mmWave communications, respectively, by 22.4% and 47.9% in spectral efficiency and 19.9% and 101% in energy efficiency.