This paper proposes a gain-scheduling robust model predictive control (GS-RMPC) algorithm for the path-following problem of autonomous independent-drive electric vehicles (AIDEVs) with consideration of time-varying and uncertainties. Firstly, the polytopic uncertainty method and norm-bounded uncertainty method are introduced to characterise the vehicle dynamics model. Secondly, the infinite predict horizon optimisation process of online GS-RMPC is transformed into a series of linear matrix inequalities (LMIs) by minimising the worst-case objective function while considering all scheduling states in the polytope. Thirdly, an offline solution is also proposed to reduce the computational burden based on asymptotically stable invariant ellipse sets. Then, a hierarchical control structure is proposed to distribute the additional yaw moment, and a multi-step predictor is designed to compensate for the actuator time delay. Finally, the hardware-in-the-loop (HIL) testing is conducted to verify the efficacy of the proposed strategy.