Large earthquakes on strike‐slip faults often rupture multiple fault segments by jumping over stepovers. Previous studies, based on field observations or numerical modeling with a homogeneous initial stress field, have suggested that stepovers more than wide would stop the propagation of rupture, but many exceptions have been observed in recent years. Here, we integrate a dynamic rupture model with a long‐term fault stress model to explore the effects of background stress perturbation on rupture propagation across stepovers along strike‐slip faults. Our long‐term fault models simulate steady‐state stress perturbation around stepovers. Considering such stress perturbation in dynamic rupture models leads to prediction of larger distance a dynamic rupture can jump over stepovers: over 15 km for a releasing stepover or 7 km for a restraining stepover, comparing with the 5 km limit in models with the same fault geometry and frictional property but assuming a homogeneous initial stress. The effect of steady‐state stress perturbations is stronger in an overlapping stepover than in an underlapping stepover. The maximum jumping distance can reach 20 km in an overlapping releasing stepover with low‐static frictional coefficients. These results are useful for estimating the maximum length of potential fault ruptures and assessing seismic hazard.