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Rare-earth indium oxides RInO₃ (R = rare earth), in which R³⁺ ions occupy two nonequivalent sites forming a honeycomb lattice with a superimposed triangular lattice (so-called stuffed honeycomb lattice), present an excellent platform to study the combination of two different frustrated lattices. Since the total angular moment L of Gd³⁺ ion is zero, GdInO₃ is expected as pure spin magnetism and may be considered as a classical Heisenberg spin system in the stuffed honeycomb lattice. A high quality isotope single crystal ¹⁶⁰GdInO₃ was synthesized for neutron scattering studies to avoid the high neutron absorption of natural Gd. The specific heat measurement shows that the compound exhibits two step magnetic phase transitions at 2.2 K and 1.08 K corresponding to two different antiferromagnetic phases that were characterized by single crystal neutron diffraction. These phases transition may be explained via the order-by-disorder mechanism.