Millimetre wave (mmWave) multiple-input multiple-output (MIMO) systems have been proposed to enable Gbps communication for next-generation cellular systems and local area networks. To compensate for the severe propagation loss of the mmWave channel, a cost-effective hybrid precoding architecture, combining a digital precoder and an analogue precoder, is widely used in mmWave MIMO systems. In this study, two hybrid precoding algorithms based on particle swarm optimisation (PSO) algorithm will be proposed for two different hybrid precoding structures, i.e. the fully connected and partially connected structures. First, the authors use the phase of the analogue precoding variable to replace the corresponding variable with the constraints of the unit norm to solve the non-convex constraints skillfully. Then they design analogue precoding by using PSO algorithm and compute the digital precoding based on the least squares solution. Finally, the proposed algorithms are compared with the existing advanced algorithms. Simulation results demonstrate that the proposed algorithms can approach the optimal performance under the corresponding structure.