Jittering effects significantly degrade the performance of UAV millimeter-wave (mmWave) communications. To investigate the impacts of UAV jitter on mmWave communications, we firstly model UAV mmWave channel based on the geometric relationship between element antennas of the uniform planar arrays (UPAs). Then, we extract the relationship between (I) UAV attitude angles & position coordinates and (II) angle of arrival (AoA) & angle of departure (AoD) of mmWave channel, and we also derive the distribution of AoA/AoD at UAV side from the random fluctuations of UAV attitude angles, i.e., UAV jitter. In beam training design, with the relationship between attitude angles and AoA/AoD, we propose to generate a rough estimate of AoA and AoD from UAV navigation information. Finally, with the rough AoA/AoD estimate, we develop a compressed sensing (CS) based beam training scheme with constrained sensing range as the fine AoA/AoD estimation. Particularly, we construct a partially random sensing matrix to narrow down the sensing range of CS-based beam training. Numerical results show that our proposed UAV beam training scheme assisted by navigation information can achieve better accuracy with reduced training length in AoA/AoD estimation and is thus more suitable for UAV mmWave communications under jittering effects.