To satisfy increased data quantity demanded by users, millimeter-wave (mmWave) communication using large bandwidth and numerous antennas has considerable promise as a new technology for wireless communication. Also, it is possible to increase more data rate by using a dual polarized array antenna (DPAA). On the other hand, beamforming techniques have to be used in mmWave communication to overcome high path-loss. Conventional beamformers, however, have problems of high costs, high power consumption, and difficulties of implementation to be used in mmWave communication. Thus, a hybrid analog radio frequency and digital baseband beamformer is used to solve these problems. Since, it is very hard to achieve perfect channel state information, it is necessary to use limited feedback information based on beam training. In this letter, a hybrid beamforming system based on DPAA considering practical antenna radiation pattern is developed in a multi-user channel environment. Furthermore, two hybrid beamforming algorithms using only limited feedback channel information are proposed and analyzed.