We have investigated the solid solution range of single phase La1-xRxRh3B (R = Gd, Lu and Sc) compounds with a cubic anti-perovskite type structure. The behaviors of lattice parameters, hardness, and thermogravimetry–differential thermal analysis (TG-DTA) were also investigated. The cubic anti-perovskite phase exists over the entire composition range x from 0.0 to 1.0 for all La-Gd, La-Lu and La-Sc systems. Both the lattice parameters and the hardness in all La-Gd, La-Lu and La-Sc systems show a linear dependence on the degree of the substitution x of La atom. The results of TG-DTA measurements indicate that oxidation of the compounds in air begins at about 500-600 K. The mixed phases of RBO3, R2O3 and Rh are identified as oxidized products around x = 0.4 to 0.6 composition. The oxidation onset temperature, and weight gains due to the oxidation depend on the degree of substitution x. The behavior of crystallographic and physical/chemical properties in the present compounds La1-xRxRh3B strongly depend on the atomic size of the rare-earth atoms that form the cubic framework.