In this paper, we investigate the system performance of a multi-cell multi-user (MU) hybrid millimeter wave (mmWave) multiple-input multiple-output (MIMO) network adopting the channel estimation algorithm proposed in [1] for channel estimation. Due to the reuse of orthogonal pilot symbols among different cells, the channel estimation is expected to be affected by pilot contamination, which is considered as a fundamental performance bottleneck of conventional multicell MU massive MIMO networks. To analyze the impact of pilot contamination on the system performance, we derive the closed-form approximation expression of the normalized mean squared error (MSE) of the channel estimation performance. Our analytical and simulation results show that the channel estimation error incurred by the impact of pilot contamination and noise vanishes asymptotically with an increasing number of antennas equipped at each radio frequency (RF) chain deployed at the desired BS. Thus, pilot contamination is no longer the fundamental problem for multi-cell hybrid mmWave systems.