Power system stabilisers (PSSs) are supplementary controllers connected to the excitation system of synchronous generators to damp electromechanical oscillations. Multi‐band PSSs are reported as advanced PSSs with the ability to damp out all oscillation modes present in the power systems. This study presents the design of a robust fractional‐order multi‐band power system stabiliser (Fo‐MBPSS) using a meta‐heuristic hybrid algorithm for dynamic stability improvement of multi‐machine power systems. The large bandwidth, memory effect and flat phase contribution in the frequency response of fractional‐order controllers are exploited to make the Fo‐MBPSS perform well against a wide range of system uncertainties. The parameter tuning problem of Fo‐MBPSS is transformed to an optimisation problem that is solved using a hybrid algorithm by combining a dynamic genetic algorithm (DGA) with a standard particle swarm optimisation (PSO) algorithm. The performance of the proposed DGA‐PSO‐Fo‐MBPSS is evaluated through eigenvalue analysis, non‐linear time‐domain simulations and some performance indices, in two different multi‐machine systems under different loading conditions and disturbances. The results are compared with PSO‐based conventional MBPSS and PSO based Fo‐MBPSS (PSO‐Fo‐MBPSS) to establish the fractional parameter effect on the improvement of the system dynamic response and the relevance of the proposed hybrid optimisation technique in achieving robustness.