Recently, H-Infinity adaptive fuzzy controller (HAFC) and its potential application in improving vehicle stability has some attention. This paper studied this application by developing a nonlinear model for the vehicle suspension mounting point displacement (SMD) and the variable geometry suspension system (VGS). The VGS model was developed by deriving the kinematic equations from the vehicle double wishbone suspension system for the vehicle handling model with eight degrees of freedom (8DOF). The limited area of the SMD necessitates the use of a proper controller, so this paper investigated the suitability of a proportional-integral-derivative controller (PID), an adaptive fuzzy controller (AFC), and HAFC for this purpose. The stability status and adaptation laws were assessed by Lyapunov synthesis and the result showed that integral of square error (ISE) achievable by HAFC for two standard maneuvers is lower than PID and AFC. The result also showed that SMD of HAFC is lower than AFC and extremely PID. The use of HAFC also resulted in the best vehicle stability, soft response and robustness.