  The crystal structure and magnetic property of the single crystalline
hexagonal rare-earth indium oxides GdInO$_3$ have been studied by combing
experiments and model calculations. The two inequivalent Gd$^{3+}$ ions form
the centered honeycomb lattice, which consists of honeycomb and triangular
sublattices. The dc magnetic susceptibility and specific heat measurements
suggest two antiferromagnetic phase transitions at $T_\textrm{N1}$ = 2.3 K and
$T_\textrm{N2}$ = 1.02 K. An inflection point is observed in the isothermal
magnetization curve, which implies an up-up-down phase with a 1/3 magnetization
plateau. We also observe a large magnetic entropy change originated from the
magnetic frustration in GdInO$_3$. By considering a classical spin Hamiltonian,
we establish the ground state phase diagram, which suggests that GdInO$_3$ has
a weak easy-axis anisotropy and is close to the equilateral triangular-lattice
system. The theoretical ground-state phase diagram may be used as a reference
in NMR, ESR, or $\mu$SR experiments in future.
