The vehicle lateral stability control is a challenging problem due to the tire nonlinearity and the immeasurable sideslip angle. Thus, an adaptive model predictive control (AMPC) scheme based on interacting multiple model (IMM) vehicle sideslip angle observer is proposed in this paper. First, the observer is composed of the Extended Kalman filter (EKF) and the Unscented Kalman filter (UKF), which improves the real-time performance as well as the observation accuracy. Then, a multi-objective controller based on adaptive vehicle model prediction is designed using model predictive control algorithm. This controller aims to achieve a balance between the actuation and state constraints. The T-S fuzzy algorithm is used to observe the tire cornering stiffness and design an adaptive vehicle model. By utilizing the appropriate objective function and a quadratic programing solver, the controller output is obtained to achieve vehicle stability control. Finally, the effectiveness of the designed AMPC scheme under various working conditions is verified by Carsim-Simulink joint simulation platform and hardware-in-the-loop (HIL) test.