The primary hot-leg piping system of the advanced sodium-cooled fast reactor under conceptual study in Japan (named Japan sodium-cooled fast reactor: JSFR) utilizes large-diameter and thin-walled pipes to ensure high coolant velocity, which inevitably leads to the occurrence of flow-induced vibration. Usually, the structural integrity of a piping system under flow-induced vibration is defined to be the maximum stress amplitude below the design fatigue limit. The present study tries to establish a reasonable methodology to estimate the high-cycle fatigue damage due to flow-induced vibration depending on its frequencies and the corresponding stress levels. An analytical procedure for probabilistic fatigue evaluation is developed and applied to the hot-leg piping system. The reasonability of the newly proposed methodology is confirmed from a test simulation.