A method for producing a Ti-Mo alloy, the method comprising the steps of: subjecting an ingot prepared by cold crucible levitation melting, consumable electrode-type vacuum arc melting, electron beam melting or plasma arc melting, and consisting of Ti, Mo and any inevitable impurities, and optionally containing at least one element for stabilizing the beta phase selected from the group consisting of Ta, Nb, W, V, Cr, Ni, Mn, Co and Fe so that the collective Mo equivalent content defined as follows: Mo equivalent = Mo content + Ta content / 5 + Nb content / 3.5 + W content / 2.5 + V content / 1.5 + Cr content × 1.25 + Ni content × 1.25 + Mn content × 1.7 + Co content × 1.7 + Fe content × 2.5, all contents being in mass %; is 10 to 20 mass %, and wherein the Mo content is 10 to 20 mass%; and wherein the remainder comprises Ti and inevitable impurities; to mechanical processing by caliber rolling, extrusion, or wire drawing in the state in which the ingot is circumferentially restrained at a temperature in the range of 600 to 1100 °C so that the cross-sectional area of the rod or wire obtained after the mechanical processing becomes 10% or less of the initial ingot cross-sectional area; subjecting the material obtained after the mechanical processing with a solution heat treatment at a temperature in the range of from the beta transformation temperature to 1,100°C so that a beta phase is solely present in the material; cooling the material obtained after solution heat treatment at a rate of 20°C/min or more so that no alpha phase is precipitated; subjecting the material after the cooling step with an ageing treatment at a temperature of 150 to 500°C for a time of from one minute to 100 hours, to precipitate an aged omega phase along the segregation portion in the plane of a backscattered electron image or an energy dispersive X-ray spectroscopy image of the Ti-Mo alloy, as examined under a scanning electron microscope, when measured in the plane perpendicular to the rolling direction; wherein the Ti-Mo alloy so produced has said beta phase and said aged omega phase; wherein the Ti-Mo alloy so produced has a swirly segregation portion having a width of 10 to 20 μm in the plane of a backscattered electron image or an energy dispersive X-ray spectroscopy image of the Ti-Mo alloy, as examined under a scanning electron microscope, when measured in the plane perpendicular to the rolling direction, in which the Mo content is larger than the collective Mo content of the Ti-Mo alloy. subjecting an ingot prepared by cold crucible levitation melting, consumable electrode-type vacuum arc melting, electron beam melting or plasma arc melting, and consisting of Ti, Mo and any inevitable impurities, and optionally containing at least one element for stabilizing the beta phase selected from the group consisting of Ta, Nb, W, V, Cr, Ni, Mn, Co and Fe so that the collective Mo equivalent content defined as follows: Mo equivalent = Mo content + Ta content / 5 + Nb content / 3.5 + W content / 2.5 + V content / 1.5 + Cr content × 1.25 + Ni content × 1.25 + Mn content × 1.7 + Co content × 1.7 + Fe content × 2.5, all contents being in mass %; is 10 to 20 mass %, and wherein the Mo content is 10 to 20 mass%; and wherein the remainder comprises Ti and inevitable impurities; to mechanical processing by caliber rolling, extrusion, or wire drawing in the state in which the ingot is circumferentially restrained at a temperature in the range of 600 to 1100 °C so that the cross-sectional area of the rod or wire obtained after the mechanical processing becomes 10% or less of the initial ingot cross-sectional area; is 10 to 20 mass %, and wherein the Mo content is 10 to 20 mass%; and wherein the remainder comprises Ti and inevitable impurities; to mechanical processing by caliber rolling, extrusion, or wire drawing in the state in which the ingot is circumferentially restrained at a temperature in the range of 600 to 1100 °C so that the cross-sectional area of the rod or wire obtained after the mechanical processing becomes 10% or less of the initial ingot cross-sectional area; subjecting the material obtained after the mechanical processing with a solution heat treatment at a temperature in the range of from the beta transformation temperature to 1,100°C so that a beta phase is solely present in the material; cooling the material obtained after solution heat treatment at a rate of 20°C/min or more so that no alpha phase is precipitated; subjecting the material after the cooling step with an ageing treatment at a temperature of 150 to 500°C for a time of from one minute to 100 hours, to precipitate an aged omega phase along the segregation portion in the plane of a backscattered electron image or an energy dispersive X-ray spectroscopy image of the Ti-Mo alloy, as examined under a scanning electron microscope, when measured in the plane perpendicular to the rolling direction;