High‐quality In1-xGaxP epitaxial layers were grown on GaAs0.61P0.39 substrates by liquid‐phase epitaxy using a supercooling technique. The growth conditions and properties of the undoped In1-xGaxP layers are described in detail. The lattice mismatch normal to the wafer surface between the In1-xGaxP layer and GaAs0.61P0.39 substrate varies linearly with the supercooled temperature of the growth solution. Low‐carrier‐concentration undoped epitaxial layers can be grown from an In solution baked at temperature higher than 900 °C for 10 h and with a suitable supersaturation temperature. The lowest carrier concentrations of 8–20×1015 cm-3 measured by the capacitance‐voltage method have been achieved in the layers grown with a 9–12 °C supercooled temperature. These samples with a lattice mismatch of ∼+0.15% also show the narrowest full widths at half maximum of photoluminescence peaks of 36 meV at 300 K, 11.5 meV at 16 K, and 7.5 meV at 4.5 K. The electrical and optical properties of the In1-xGaxP epitaxial layers are better than those reported previously. From the above results, the optimum growth condition could then be determined.