In this paper, a novel hybrid beamforming (HBF) design utilizing a pre-defined virtual grouping (PDVG) algorithm is proposed for the uplink (UL) multi-user (MU) multiple-input multiple-output (MIMO) millimeter wave (mmWave) systems. The computational complexity of achieving traditional MU-MIMO beamforming (BF) methods in the mmWave systems becomes significant due to the hardware constraints. Thus, the proposed HBF-PDVG algorithm aims to reduce the feedback overhead by employing a three-phase algorithm. The essential idea is to perform the user selection independently from the HBF design by utilizing the PDVG algorithm after completing the analog BF training and then mitigating the remaining MU interference among the selected users using digital BF. Simulation results demonstrate the significant sum-rate benefits of the HBF-PDVG algorithm compared with zero-forcing (ZF) and random selection algorithm methods.