An anti-rollover apparatus and control method for heavy-duty vehicles with a pneumatic brake system includes an anti-yaw module, an anti-roll module, an electronic control unit (ECU) (10), a yaw velocity sensor (12), and a vehicle roll angle sensor (18). The ECU (10) controls solenoid valves (4, 9, 11, 19, and 24) to achieve braking of part of wheels to obtain anti-yaw torques and improve the yaw stability of the heavy-duty vehicles. The ECU (10) controls gas switch valves (21 and 22) to spray high-pressure gases recovered in brake chambers (1, 13, 16, and 26) out, anti-roll torques are obtained through the jet reactive force, and the roll stability of the heavy-duty vehicles is improved.