While hydrogen is one of plausible major light elements in the core, the high-temperature equation of state (EoS) of Fe-H alloy has not been experimentally examined to the core pressure range. Here we measured the volume (V) of non-magnetic (NM) fcc FeH at high pressure and temperature (P-T) to 142 GPa and 3660 K in a laser-heated diamond-anvil cell (DAC) and obtained its P-V-T EoS. An increase in the lattice volume of Fe per H atom, ΔVH, determined as functions of P and T is found to be substantially smaller than the volume of metallic H that has been used to estimate H concentration in Fe-H alloy. The ΔVH is almost identical between fcc and dhcp phases in the NM state, suggesting that it is applicable to hcp. The extrapolation of ΔVH to inner core conditions indicates its maximum H content to be 0.8–0.9 wt%.