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To rank the pulse-like ground motions based on the damage potential to different structures, the internal relationship between the damage potential of pulse-like ground motions and engineering demand parameters (<i>EDPs</i>) is analyzed in this paper. First, a total of 240 pulse-like ground motions from the NGA-West2 database and 16 intensity measures (<i>IMs</i>) are selected. Moreover, four reinforced concrete frame structures with significantly different natural vibration periods are established for dynamic analysis. Second, the efficiency and sufficiency of the <i>IMs</i> of ground motion are analyzed, and the <i>IMs</i> that can be used to efficiently and sufficiently evaluate the <i>EDPs</i> are obtained. Then, based on the calculation results, the principal component analysis (PCA) method is employed to obtain a comprehensive <i>IM</i> for characterizing the damage potential of pulse-like ground motions for specific building structures and <i>EDPs</i>. Finally, the pulse-like ground motions are ranked based on the selected <i>IM</i> and the comprehensive <i>IM</i> for four structures and three <i>EDPs</i>. The results imply that the proposed method can be used to efficiently and sufficiently characterize the damage potential of pulse-like ground motions for building structures.