Pulse‐like ground motions significantly influence structural responses, indicating that more consideration should be given to the seismic design of structures in the near‐site region. However, less effort focuses on the seismic response of a cable‐stayed bridge under near‐field pulse‐like excitations, and the difference in structural responses caused by near‐field pulse‐like and far‐field ground motions is not fully captured. This paper, therefore, aims to investigate the effect of pulse‐like ground motions on a cable‐stayed bridge, and it presents a comparison of far‐field earthquakes. Considering the finite number of recorded ground motions, artificial pulse‐like ground motions are adopted in this study. Furthermore, two classical intensity measures (peak ground velocity [PGV] and peak ground acceleration) were used to establish the probabilistic seismic demand model for cable‐stayed bridges. Then, fragility curves associated with the pylon of the bridge were compared under the action of different types of excitations, and the damage state of the whole pylon is presented through the median point of the slight damage of the curvature of each pylon section. The results indicate that the bottom section of the pylon is damaged first under different seismic excitations, with the PGV as the index. Moreover, far‐fault ground motions have a greater impact on the curvature response of the longitudinal bridge section of the pylon than the near‐fault ground motions, so the damage is more serious.