In the past few years, studies have focused on the use of millimeter wave (mmWave) communication as a promising technology for future cellular communication. The mmWave system requires a large number of transmit antennas to compensate for the transmission loss at higher carrier frequencies which leads to high complexity and power consumption. To overcome these difficulties, hybrid precoding that combines analog and digital precoding with a reduced number of RF chains is widely studied. We propose a hybrid beamforming scheme with partial interfering beam feedback for a codebook-based multi-user multiple-input multiple-output (MU-MIMO) system, where users feedback information only about the top-p transmit beams. For the analog part of the precoding, we consider beamforming using the pre-defined codebook. For the digital part, we approximate the effective channel and propose both linear and non-linear precoding techniques. The linear precoder is based on zero-forcing (ZF) and the non-linear precoder is based on Tomlinson Harashima Precoding (THP). We also propose an iterative method for robust MU-MIMO THP design that minimizes the total transmit power under mean square error constraints at each user. Numerical results show that the proposed hybrid beamforming performs better than an existing hybrid precoding scheme based on channel reconstruction.