Millimeter-wave (mmWave) massive multiple-input multiple-output (MIMO) systems utilize hybrid beamforming techniques to alleviate the implementation complexity of combining a large number of antennas. In this paper, we propose a hybrid processing algorithm via matrix decomposition for mmWave massive MU-MIMO systems. Both inter-user interference (IUI) and inter-stream interference (ISI) within the user are taken into consideration. We derive a closed-form expression of digital and analog precoder/combiner to achieve nearlyoptimal performance. In the large system analysis, we prove that the proposed algorithm can obtain unconstrained optimal performance when the number of antennas is infinite. The results indicate that the proposed algorithm outperforms other existing hybrid designs in terms of BER and sum-rate.