Millimeter wave - mm Wave - communications has been considered as a key authorised technology for the fifth generation networks. Hybrid precoding, which refer to a blend of analog and digital precoding, can achieve high spectral and energy efficiencies. However a cost-effective alternative and power consumption are needed. So hybrid precoding strategies become promising solutions. In the higher carrier frequencies, especially the millimeter-wave range, there are significant degradations in the transmitted and received signals due to radio-frequency impairments such as phase noise introduced by the local oscillators (LO), which is the irregular difference among the phase of the local oscillator and the phase of the carrier signal. It's becoming a limiting factor in high data rate digital communication systems. In this research, we study the impact of phase noise on the performance of hybrid precoding structure in millimeter wave Multiple-Input Multiple-Output (MIMO) (mmWave MIMO) systems. Manifold optimization based alternating minimization algorithm is proposed. An optimization problem is formulated for phase noise issue in millimeter wave MIMO system. Results show that the impact of phase noise can degrade the system performance at higher RF chains.