A 1D metallic surface state was created on an anisotropic InSb(001) surface covered with Bi. Angle-resolved photoelectron spectroscopy (ARPES) showed a 1D Fermi contour with almost no 2D distortion. Close to the Fermi level (E_{F}), the angle-integrated photoelectron spectra showed power-law scaling with the binding energy and temperature. The ARPES plot above E_{F}, obtained thanks to a thermally broadened Fermi edge at room temperature, showed a 1D state with continuous metallic dispersion across E_{F} and power-law intensity suppression around E_{F}. These results strongly suggest a Tomonaga-Luttinger liquid on the Bi/InSb(001) surface.