In millimeter-wave (mmWave) networks, where faster signal attenuation is compensated by the use of highly directional antennas, the effects of high mobility may seriously harm the link quality and, hence, the overall system performance. In this paper, we study the channel access in unlicensed mmWave networks with mobile clients, with particular emphasis on initial beamforming training and beam refinement protocol as per IEEE 802.11ad/ay standard. We explicitly model beamforming procedures and corresponding overhead for directional mmWave antennas and provide a method for maximizing the average data rate over the variable length of the 802.11ad/ay beacon interval in different mobility scenarios. We illustrate the impact of the client speed and mobility patterns by examples of three variations of the discrete random walk mobility model. © 2019, Springer Nature Switzerland AG.