This paper presents a novel observer-based gain-scheduling path following control algorithm for autonomous electric vehicles subject to time delay. Firstly, the lateral dynamic model of the autonomous electric vehicle is constructed by a polytope with four vertices, in which the issues of the time-varying longitudinal velocity and nonlinear tyre dynamics are accurately described. Secondly, taking the time delay encountered in the process of signal transmission into consideration, the observer-based path following controller is proposed by using easily measured vehicle states. In the algorithm, the observer and controller gains are gain scheduled according to the actual longitudinal velocity. Thirdly, based on Lyapunov stability theory, an appropriate Lyapunov–Krasovskii functional is constructed to derive sufficient conditions of the controller, which is effective to ensure the asymptotical stability of the closed-loop path following error system with a guaranteed (Formula presented.) performance. Specially, for ease of computation, the sufficient conditions of controller design are developed in terms of a set of linear matrix inequalities. Finally, numerical simulations are implemented to illustrate the efficiency and superiority of the proposed method in comparison with the existing method.