To meet the explosive growth of mobile traffic, it is necessary to guarantee high data rate in today's communication system. One of the methods to support high data rate is to use wide bandwidth (spectrum). Due to the limitation of frequency spectrum for the commercial usage, we choose millimeter-Wave (mmW) band of 30GHz and exploit analogue beamforming technique, focusing electro-magnetic wave energy at a certain direction, not an omni-direction. In the analogue beamforming technique, beam selection is required so that base station (BS) and mobile station (MS) communicate with the best beam each other and this procedure is performed periodically for the selected beams not to be mis-aligned. To extend battery lifetime of user equipment, current broadband system such as 3GPP LTE/LTE Advanced adopts discontinuous reception (DRX) which the new mmW system needs too. Therefore, we propose the DRX mechanism considering analogue beamforming technique and analyze the performance of the system varying parameters of beam selection and DRX according to the given beam pattern, traffic model and movement of MS.