By exploiting the degree of freedom on the altitude, unmanned aerial vehicle (UAV) communication can provide ubiquitous communication for future wireless networks. In the case of concurrent transmission of multiple UAVs, the directional beamforming formed by multiple antennas is an effective way to reduce co-channel interference. However, factors such as airflow disturbance or estimation error for UAV communications can cause the occurrence of beam misalignment. In this paper, we investigate the system performance of a multi-tier UAV communication network with the consideration of unstable beam alignment. In particular, we propose a tractable random model to capture the impacts of beam misalignment in the 3D space. Based on this, by utilizing stochastic geometry, an analytical framework for obtaining the outage probability in the downlink of a multi-tier UAV communication network for the closest distance association scheme and the maximum average power association scheme is established. The accuracy of the analysis is verified by Monte-Carlo simulations. The results indicate that in the presence of random beam misalignment, the optimal number of UAV antennas needs to be adjusted to be relatively larger when the density of UAVs increases or the altitude of UAVs becomes higher.