Tire blowout strongly affects vehicle stability and road safety by introducing sudden and intensive tire force disturbances. In such an emergent event, vehicles equipped with an automatic controller for normal path following (i.e., SAE driving automation level 2/3) may have degraded performance, which requires cooperation with a human driver. Considering a panicked driver could perform improper or wrong operations, this paper proposes a novel trust-based shared steering control for vehicle stabilization after tire blowout. Based on specific and crucial factors in tire blowout events, the driver’s steering input and the resulting driver’s fault and performance are comprehensively evaluated in a designed controller-to-human (C2H) trust module. The real-time computational trust simultaneously adjusts the cooperative level in a dynamic control authority allocation function. Matlab/Simulink and CarSim^® co-simulation results validate that the proposed shared control can effectively enhance vehicle stability and driving safety after tire blowout, even with the faulty and excessive steering inputs from a panicked driver.