The isothermal section of the Lu-Fe-Ga ternary system at 773K was investigated and constructed based on X-ray powder diffraction analysis. Thirteen binary compounds, Lu2Fe17, Lu6Fe23, LuFe2, LuGa3, LuGa2, Lu3Ga5, LuGa, Lu3Ga2, Lu5Ga3, Fe3Ga, Fe6Ga5, Fe3Ga4, FeGa3, nine ternary solid solutions, T-1-LuFe2-1.43Ga0-0.57, T-2-LuFe1.34-0.92Ga0.68-1.08, T-3-LuFe0.52-0.26Ga1.48-1.74, T-5-LuFe2.04-1.72Ga0.96-1.28, T-6-Lu6Fe23-21.4Ga0-1.6, T-7-Lu2Fe17-14.5Ga0-3.5, T-8-Lu2Fe12.9-8.1Ga4.1-8.9, T-9-LuFe6.8-5.5Ga5.2-6.5, T-10-LuFe5.2-4.5Ga6.8-7.5, and two ternary compounds, T-4-LuFe2.35Ga0.65 and T-11-Lu2FeGa8 have been confirmed. The structures of the five new ternary compounds or solid solution T-2, T-3, T-4, T-5 and T-8 are determined by Rietveld refinement method.