We examined the density, bulk sound (compressional) velocity, and Grüneisen parameter of liquid pure Fe, Fe100H28 (0.50 wt % H), Fe88H40 (0.81 wt % H), and Fe76H52 (1.22 wt % H) at Earth's outer core pressure and temperature (P‐T) conditions (~100 to 350 GPa, 4000 to 7000 K) based on first‐principles molecular dynamics calculations. The results demonstrate that the thermodynamic Grüneisen parameter of liquid iron alloy decreases with increasing pressure, temperature, and hydrogen concentration, indicating a relatively small temperature gradient in the outer core when hydrogen is present. Along such temperature profile, both the density and compressional velocity of liquid iron containing ~1 wt % hydrogen match seismological observations. It suggests that hydrogen could be a primary light element in the core, although the shear velocity of the inner core is not reconciled with solid Fe‐H alloy and thus requires another impurity element. Key Points Liquid Fe‐H alloys under the outer core conditions are calculated by first principles Approximately 1 wt % hydrogen concentration is found to reproduce density and bulk sound velocity of PREM Gruneisen parameter depends on hydrogen concentration