The seismic response of the structure isolated by friction pendulum system(FPS)with an asymmetric superstructure under bilateral ground motions is analyzed.The effects of the eccentricity and the torsional stiffness on the superstructure are studied.It is shown that the effect of the eccentricity of the superstructure on the displacement and the acceleration of the superstructure and the isolation layer is remarkable.Even though the eccentricity is small,the effect of which should be taken into account in the seismic design of the base-isolated structure.The effect of the torsional stiffness of the superstructure on the seismic response of the superstructure is more remarkable than that on the seismic response of the isolation layer.So the seismic response of the superstructure can be effectively diminished by decreasing the eccentricity and increasing the torsional stiffness of the superstructure.