The chemical composition of carbonaceous chondrites permits up to 0.50.4wt%N in the Earth's core, which potentially affects the melting temperature, density profile, and phase relation of the core iron alloy. Here we have determined the melting curve and the high-temperature equation of state (EoS) of -Fe7N3, which is stable above 40GPa as the most Fe-rich iron-nitride. Experiments were performed in a laser-heated diamond-anvil cell up to 136GPa, together with synchrotron X-ray diffraction measurements. We found that multiple melting criteria gave similar melting temperatures: (1) the appearance of diffuse X-ray scattering, (2) discontinuity in the laser power versus temperature relation, and (3) the reduction in diffraction peak intensity from solid. The validity of these melting criteria was confirmed by textural observation of recovered samples. We also observed rapid recrystallization at temperatures lower than the melting temperatures. The results demonstrate that -Fe7N3 melts congruently at about 3,100K at 135GPa, lower than the melting temperatures of FeSi and FeO and similar to that of FeS. The thermal EoS indicates that the density of Fe-7(C,N)(3) matches the observed inner core density. Combining the melting curve and the EoS of -Fe7N3, we also obtain the EoS of liquid Fe7N3. It shows that the density and compressibility of Fe+10wt%N is compatible with the outer core density profile. It supports the presence of some nitrogen in the liquid and solid parts of the core, although its concentration is difficult to constrain from the core density.