To investigate the ground motion intensity measures suitable for evaluating high-rise structures under near-fault ground motions with pulse-like effect, this paper proposes a new ground motion intensity measure considering period elongation effect and higher mode effect based on acceleration spectrum. Taking two high-rise reinforced chimney structures (120 m and 240 m) as research objects, the correlation between damage indices (ParkAng damage index, maximum inter-story drift ratio, maximum structural curvature, maximum floor acceleration, and maximum roof displacement) of high-rise structures and 37 ground motion intensity measures was studied under near-fault ground motions using OpenSEES. Results show that the proposed intensity measure was the optimal index in predicting the ParkAng damage of high-rise concrete structures under near-fault ground motions. High correlation between velocity-related intensity measures and structural damage index was observed. As the structural period increased, the correlation between damage indices and displacement-related intensity measures was improved. Besides, peak ground acceleration had limitations in characterizing the deformation and failure of high-rise structures, but it could be used to analyze the seismic performance of non-structural components. The research results can provide reference for selecting proper measures and structural damage indices to evaluate the seismic performance of high-rise structures under near-fault ground motions.