This study aimed at proposing a new ground motion scaling method for precise spectral matching between the response accelerations and the standard design spectrum regarding the normalization procedure. In this method, the dispersion in acceleration and displacement responses were decreased significantly. Moreover, 11 parameters were used for normalizing response accelerations, including peak ground acceleration, peak ground velocity, peak ground displacement, Arias intensity, Housner intensity, cumulative absolute velocity, maximum incremental velocity, energy index, acceleration spectrum intensity, velocity spectrum intensity, and specific energy density. Three sets of non-pulse-like, near-field pulse-like and non-pulse-like long-duration ground motions were taken into account to investigate the effect of earthquake characteristics on normalizing parameters. Hence, by performing sensitivity analysis, suitable parameters were determined for normalizing response accelerations. Statistical results illustrated that normalizing response accelerations to acceleration spectrum intensity, Housner intensity, and peak ground displacement led to minimum dispersion at acceleration-sensitive, velocity-sensitive, and displacement-sensitive regions, respectively. Moreover, the results showed that suitable normalizing parameters could be determined considering the period of vibration. It was concluded that normalizing response accelerations and scaling of them could lead to appropriate spectral matching and low dispersion. Finally, drift dispersion for four, eight, and twelve-story steel special concentrically braced frame structures under nonlinear fiber-element time-history analysis was evaluated carefully. The results indicated that the inter-story drift dispersion decreased acceptably in all structures.