This paper shows the feasibility of the displacement-dependent damper for a base-isolated structure. The ideal displacement-dependent damper can be modelled by using complex damping. To simulate such dampers by a semi-active damper (in this study the magneto-rheological damper), the pseudo-complex- damping rule is considered. From a series of shaking table tests and numerical analyses for the base-isolated structure, incorporated with the semi-active damper controlled by the pseudo-complex-damping rule in the base-isolated layer, it is shown that the hysteretic behavior of the damper, by the pseudo-complex-damping rule, cannot simulate the ideal displacement-dependent damper well because of the simplified assumption for the rule. An improvement of the pseudo-complex-damping rule is considered, and it is shown from the analyses that the damper by the improved rule can better simulate the displacement-dependent damper.