The roll dynamic model of counterbalance forklift trucks that takes into account the hierarchical rolling process is proposed. The influence of vehicle speed on the critical instability characteristics is investigated under various steering angles using bifurcation theory. Then, a novel rollover index for forklift trucks is established utilizing dominant factors in both steering and traveling over obstacle scenarios. Subsequently, a hierarchical anti-rollover control scheme is formulated based on both the degree of instability and the output characteristics of the hydraulic actuator. In addition, an adaptive model predictive control (MPC) system is designed for adjusting the output force of the hydraulic cylinder and regulating the steering ratio. The simulation and experimental results indicate that the proposed comprehensive rollover index can continuously characterize the rolling state of the forklift truck when the wheels lift-off. Furthermore, the designed control framework yields superior performance for anti-rollover control under steering conditions.