Abstract: In this paper, inter-story shear model of the asymmetric base-isolated structure is built, which incorporates the deformation of each isolation bearing. And a methodology is developed to simulate simultaneously bi-axial near-fault pulse-like and far-field ground motions, Under both near-fault pulse-like and far field ground motions, the nonlinear dynamic responses of the asymmetric base-isolated structure are investigated comparatively. Seismic responses are closely related with isolation eccentricity, superstructure eccentricity, ratio of torsional-to-lateral frequency of superstructure, and pulse period of near-fault pulse-like ground motions, whose effects are discussed in this paper. Results show that the asymmetric base-isolated structure with isolation eccentricity is more vulnerable to near-fault pulse-like ground motions, and its seismic response is mainly governed by the pulse period of near-fault pulse-like ground motions.