Lens-based millimetre-wave (mmWave) massive multiple-input multiple-output (MIMO) can utilise beam selection to reduce the number of radio-frequency (RF) chains. However, most of the existing beam selection schemes involve high complexity, especially with the fast time-variant mmWave channels. In this Letter, by exploiting the mmWave channel property that the angles of departure of channel paths are slowly varying, the authors propose an adaptive neighbourhood search (ANS) beam selection. The key idea is to utilise the concept of neighbourhood search developed from machine learning to select the beams with significantly reduced complexity, where the neighbourhood range is adaptively adjusted to avoid the local optimum. Simulation results show that the authors' scheme can achieve the performance close to the conventional real-time beam selection schemes.