We examined the compression behavior of hexagonal-close-packed (hcp) (Fe0.88Si0.12)(1)H-0.61 and (Fe0.88Si0.12)(1)H-0.79 (in atomic ratio) alloys up to 138 GPa in a diamond anvil cell (DAC). While contradicting experimental results were previously reported on the compression curve of double-hcp (dhcp) FeHx (x approximate to 1), our data show that the compressibility of hcp Fe0.88Si0.12Hx alloys is very similar to those of hcp Fe and Fe0.88Si0.12, indicating that the incorporation of hydrogen into iron does not change its compression behavior remarkably. The present experiments suggest that the inner core may contain up to 0.47 wt% hydrogen (FeH0.26) if temperature is 5000 K. The calculated density profile of Fe0.88Si0.12H0.17 alloy containing 0.32 wt% hydrogen in addition to geochemically required 6.5 wt% silicon matches the seismological observations of the outer core, supporting that hydrogen is an important core light element.