The velocity pulse and displacement fling-step pulse signatures may be present in a nearfield earthquake ground motion record. It is generally known that near-field ground motion with pulse effects accelerated the building drift. The damage of building can also occur as a result of two or three earthquakes within the building's lifespan. The repeated earthquakes could cause minor to severe damage to the building, including structural collapse. This includes earthquakes with flingstep pulse, which impact is underexamined in the existing studies. Therefore, the objective of this study is to assess the impact of repeated earthquakes with displacement of the fling-step pulse on the near-collapse probability of 5-, 10-, 15 and 20-story concrete frames. Based on the response modification factor R = 8, 5, and 3, the frames are classified as special, intermediate, and ordinary, respectively. The result shows that the near-collapse probability of repeated earthquakes is more likely to occur on the concrete frames which reaches intensity measure of 27.0% than the effect of single earthquakes.