In this paper, we propose an adaptive beam search algorithm for the initial alignment of millimetre-Wave beams. The proposed algorithm works by gradually deactivating beams that are unlikely the best beam from a pre-synthesised codebook to save overhead, based on a Bayesian probability criterion with a uniform improper prior. The beam deactivations can be implemented with low-complexity operations that require computing a low-degree polynomial or a search through a look-up table. The proposed algorithm does not require prior knowledge of channel statistics or signal to noise ratios (SNRs) to optimise the amount of searching time, and uses a suitable amount of time to achieve satisfactory beam search accuracy in different SNRs and fading scenarios. Numerical results confirm that the proposed algorithm can adapt to a wide range of channels with a fixed algorithm parameter, and can achieve better balance between beam search overhead and accuracy than non-adaptive approaches with fixed overhead.