In recent decades, global seismic observations have identified increasingly complex anisotropy of the Earth’s inner core. Numerous seismic studies have confirmed hemispherical variations in the inner core’s anisotropy. Here, based on ab initio molecular dynamics calculations, we report how the anisotropy of hexagonal close-packed (hcp)-iron, under inner core conditions, could be altered when alloyed with light elements. We find that light elements in binary allows with iron — hcp-Fe-X (X = C, O, Si, and S) — could have significant effects on density, sound velocities, and anisotropy, compared with the behavior of pure hcp-iron; the anisotropy of these binary alloys depends on combined effects of temperature and the particular alloying light element. Furthermore, the change in anisotropy strength with increasing temperature can be charted for each alloy. Alloying pure iron with some light elements such as C or O actually does not increase but decreases core anisotropy at high temperatures. But the light element S can significantly enhance the elastic anisotropy strength of hcp-Fe.