Abstract: Viscosity is a key physical property that governs the dynamics and evolutionary history of the Earth inner core and plays an important role in the origin of seismic anisotropy. Previous studies have investigated the viscosity of pure iron in the hexagonal close-packed (HCP) and body-centered cubic (BCC) phases under inner-core conditions through computational simulations. However, the inner core also contains light elements such as carbon, hydrogen, oxygen, sulfur, and silicon, and the effect of these light elements on the viscosity of the inner core remains insufficiently understood. In this study, we constructed a neural-network potential (NNP) for Fe-S alloy under inner core conditions and employed it to perform large-scale molecular dynamics simulations. We systematically examined the effect of vacancy concentrations as low as 0.02% on the ionic transport properties of Fe-S alloy. Based on the self-diffusion coefficients of Fe atoms in the lattice, we further explored the creep mechanisms and viscosity of Fe-S alloys under core conditions. The results indicate that dislocation creep dominates the rheological behavior, yielding viscosities in the range of 1×10¹⁴-2×10¹⁶ Pa·s, which are consistent with constraints from free-core nutation and seismic observations.