To reasonably select a suitable set of ground motion parameters and effectively reduce the uncertainty of structural damage prediction, various ground motion parameters were preferentially selected based on the elastic network regression technique. First, the elastic network regression model was established based on various ground motion parameters and the seismic capacity of a generic set of single-degree of freedom (SDOF) systems obtained from the results of incremental dynamical analysis. Second, the values of regression coefficients in the elastic network regression model and the number of times that the regression coefficients have non-zero values were used to define the sensitivity and frequency of ground motion parameters, respectively. Third, the ranking of ground motion parameters used for seismic capacity prediction was established in terms of sensitivity and frequency of ground motion parameters obtained from the results of elastic network regression on a generic set of SDOF systems. Results were statistically organized to evaluate the influence of various ground motions, structural types and structural limit-states. The analysis result obtained from an 8-story steel frame verified that the use of ground motion parameters selected based on elastic network regression can effectively reduce the uncertainty of structural damage prediction. In addition, results showed that the standard deviation of the residuals in the regression analysis for different structural limit-states was significantly reduced when the representative ground motion parameters were employed in the least squares regression model. Moreover, representative ground motion parameters that are less affected by various ground motions, structural types and structural limit-states were selected based on the ranking results obtained from a generic set of SDOF systems. Findings of this study can provide a theoretical basis for the comparison of ground motion parameters used for the prediction of structural seismic capacity.