Hybrid precoding, combining the digital and analogue precoding, is a key enabler to reach a compromise between system performance and hardware complexity in millimetre wave (mmWave) massive multiple-input multiple-output (MIMO) systems. Most previous studies on hybrid precoding considered narrowband channels. However, mmWave systems are expected to operate on wideband channels with frequency selectivity. In this study, the authors focus on the hybrid precoding design in mmWave massive MIMO systems using orthogonal frequency division multiplexing (OFDM). By transforming the hybrid precoding problem into a series of sub-problems, they propose a low-complexity algorithm to design the digital precoder and analogue precoder alternately. In particular, a phase pursuit method is introduced to seek this solution of analogue precoding matrix with the constant amplitude constraint. Simulation results and complexity evaluations reveal that the proposed algorithm can obtain better performance and lower complexity than some existing solutions in mmWave OFDM systems.