The phase relations of an Fe10wt%Ni alloy were investigated in a diamond anvil cell up to 86 GPa and 2382 K. Adding nickel into iron stabilizes the fcc phase to higher pressures and lower temperatures compared to pure iron, and a region of two-phase coexistence between fcc and hcp phases is observed. Iron with up to 10 wt% nickel is likely to be in the hcp structure under inner core conditions. The axial ratio (c/a) of hcp-Fe10wt%Ni has a weak pressure dependence, but it increases substantially with increasing temperature. The extrapolated c/a ratio at ~5700 K and ~86 GPa is approximately 1.64, lower than a theoretically predicted value of nearly 1.7 for hcp-Fe at 5700 K and inner-core pressure. A lower c/a ratio should have an effect on the longitudinal anisotropy of the hcp phase, and hence, may influence the interpretation of the seismic wave anisotropy of the inner core.