Scanning tunneling microscopy (STM) and spectroscopy (STS) are used to study electronic states at the edges of the circular pits on the hydrogen-etched graphite surface. The edge surface state revealed by tunneling spectroscopy appears as the maximum of the local density of states (LDOS) in the energy range of 90-250 meV above the Fermi level. The dispersion of the energy state is explained by the band broadening in AB stacked H-terminated graphite. The magnitude of the edge state decreases with the distance from the pit edge as theoretically predicted.