In this study, a new damping reduction equation is proposed to obtain reasonable estimates of the actual nonlinear responses of seismic isolated structures (SIS) subjected to near fault ground motions (NFGM) with forward-rupture-directivity effect, using equivalent linear analysis (ELA) procedure. For this purpose, first, a set of 29 NFGM are selected and grouped according to their site soil classification. Then, the average response spectra of the NFGM are plotted and a smoothed design response spectrum for each set of ground motions are obtained. Next, nonlinear time history analysis (NLTHA) and ELA of SIS are performed for the selected ground motions. Subsequently, the average of the isolator displacements calculated from the NLTHA are obtained for each set of NFGM considered in the analyses. Then, the damping reduction factor required to obtain an isolator displacement equal to the average isolator displacements obtained from the NLTHA of SIS is back calculated via the ELA procedure. Next, the variation of the damping reduction factor is plotted as a function of various combinations of the parameters considered in this research in dimensionless form and nonlinear regression analyses are performed to formulate the damping reduction equation. The isolator characteristic strength, post elastic period, the corner period of the response spectrum and peak ground acceleration are found to affect the damping reduction factor and hence, the displacements obtained from ELA. The proposed damping reduction equation is found to yield more reasonable estimates of the actual nonlinear responses compared to those available in the literature and design codes.