In order to enhance the speed tracking performance of brushless direct current motor (BLDCM), a new generalised predictive fractional‐order PI (GPFOPI) control algorithm ground on lion swarm optimisation (LSO‐GPFOPI) is proposed in this paper. First, GPFOPI combines robust generalised predictive control with scalable fractional‐order PI, whose optimal control law is obtained through the model parameters and the predicted speed reference values. Next, the lion swarm algorithm is utilised to optimally tune the three parameters KP,KI,λ ${K}_{P},{K}_{I},\lambda $ of GPFOPI, so as to make them be optimised. Finally, the optimal control signal is input into the system of BLDCM to control its speed. To verify the effectiveness of LSO‐GPFOPI, its performance is compared with other algorithms. The results show that LSO‐GPFOPI has better response speed, speed tracking ability, anti‐interference ability, robustness, and self‐adaptability than other algorithms. Moreover, an experimental platform of the BLDCM drive system is built to verify the feasibility of the LSO‐GPOPI algorithm, and the test results prove that LSO‐GPOPI can guarantee the smooth and accurate operation of BLDCM.