Excessive lateral and roll motions of a high-speed train might endanger its operational safety. This paper investigates how to suppress those motions via an active-suspension method. By exploiting the structural properties of the system model and the triangular control gain, a new control scheme capable of attenuating immeasurable disturbances, compensating modeling uncertainties, and accommodating actuation faults is developed. Compared with most existing methods, the proposed method does not require precise information on the suspension parameters and the detail system model. Moreover, the magnitude of the actuation fault and the time instant at which the actuation fault occurs are not needed in setting up and implementing the proposed control scheme. The controller is tested and validated via computer simulations in the presence of parametric uncertainties and varying operation conditions.