Fling-step and forward directivity, which can impose unexpected seismic demands on structures, are the main consequences of near-fault earthquakes. Although the adverse effect of forward directivity on structures behavior is determined to some level, the influence of fling-step (static offset) on the seismic response of structures has not been extensively investigated. Given the contradictory results reported in the few available studies, further investigation on the effect of fling-step on the seismic behavior of tall buildings seems important. To this end, the ground motion record at the Heathcoat Valley Primary School station from the 2011 New Zealand earthquake with fling-step has been selected. Subsequently, various single-degree-of-freedom systems with different fundamental period values have been considered and the displacement demands of each structure subjected to the ground motion record with and without fling-step have been investigated. The results show that the demands imposed on the structures without fling-step are relatively higher in some cases. It is shown that the amount of variability in the seismic demands can depend on the ration of the fundamental period of the structure to the period of the fling-pulse.