Evaluation of structural performance under seismic excitations from low intensity to high intensity is essential to verify the seismic resistant capacity of a structure, and usually carried out by the incremental dynamic analysis (IDA) method or pushover method. The recently developed endurance time (ET) method is another method that uses dynamic pushover excitations, i.e., endurance time acceleration function, to obtain results similar to those obtained by IDA or pushover methods with low computational cost and acceptable accuracy. This study proposes an improvement on the ET method by considering more restrictions for both the elastic and inelastic response spectra in the generation procedure, and by specifying a target duration. Four reinforced concrete frame structures with 4, 8, 12, and 16 stories are adopted to verify the accuracy of the improved method. Comparison of the results obtained by the proposed method, the ET method and the IDA method shows that the improved method has a higher accuracy than the ET method. For evaluation of structural responses under specific ground motion intensity, which is typically required in seismic design codes, the results obtained by the proposed method are compared with five commonly used ground motion selection methods, and shows the proposed method provides acceptable accuracy for engineering applications.