Viscosity is critical for controlling the dynamics and evolution of the Earth’s inner core (IC). The viscosities of hexagonal close-packed (hcp) and body-centred cubic (bcc) Fe were studied experimentally and theoretically under Earth's core conditions. However, Earth’s inner core is mainly composed of Fe-Ni alloys with some light element impurities (Si, S, C, H, O), and the influence of impurities (Ni, Si, S, C, H, and O) on viscosity is still unknown. In this study, the diffusion coefficients of Fe, Ni, Si, S, C, H, and O were calculated under IC conditions using ab initio molecular dynamics (AIMD) and deep learning molecular dynamics (DPMD) methods. Among them, C, H, and O are highly diffusive like liquids in the lattice, while Fe, Ni, Si, and S diffuse through Fe site vacancies. In binary alloys, the influence of these impurities (Ni: 12.5%, S: 3.6%, Si: 3.1%, C: 1.3%, O: 1.7%, H: 0.4% by weight) on viscosity is insignificant. Based on the dislocation creep mechanism, the predicted viscosities of the hcp Fe alloys are 1 × 10¹⁴–2 × 10¹⁶ Pa·s, which is consistent with the values predicted by free inner core nutation and seismic wave attenuation observations.