The ground motion record from near-field earthquake may have forward and backward directivity effects. The first has pulse and fling-step signatures in its velocity and displacement motions, respectively. It is well recognized that the ground motion with pulse and fling-step effects amplified the building drift larger than the ground motion with no pulse and fling-step effects. The building damage also occurs due to earthquakes that are not singly exhibited. This includes the ground motion with fling-step, which is not many studied so far, especially in comparison with ground motion with pulse effect. Therefore, the goals of this study are to find out the effect of repeated earthquakes containing fling-step on the reinforced concrete (RC) moment resisting frames (MRF) in form of interstory drift ratio (IDR) and collapse probability. The 5-, 10-, and 15-story RC frames are taking into account as special, moderate and ordinary MRF, which is based on the R-factor of R = 8, R = 5, and R = 3. Based on the result of incremental dynamic analysis, the cumulative distribution function is statistically developed to define the fragility function. This function is treated as the probability of collapse of RC frames. The result shows that the performance of RC frames induced by single ground motion containing fling-step is at least 2 times larger than the single ground motion with pulse effect. The repeated earthquakes containing fling-step effect propagate the drift of 1.32 and 1.50 times larger than single earthquake with fling-effect. These motions cause the 10- and 15-story RC frames with R = 8 to have 100% of probability of collapse.