A titanium alloy containing copper, which cannot be realized by a conventional method, is provided, having a composition in which copper is contained in titanium with no segregation, and having improved strength and hardness. In addition a method is also provided, in which the titanium alloy is produced at lower cost than in a conventional method. The α+β or β titanium alloy contains copper at 1 to 10 mass %, has a crystal phase of β and α phase or of β phase, is formed of crystal particles not more than 100 μm, and has a copper concentration per an arbitrary specified 1 mm3 portion of the crystal phase at within ±40% compared to another arbitrary specified portion. The α+β or β titanium alloy is produced by mixing 1 to 10 mass % of copper powder and the remainder of titanium alloy powder and then pressing and forming while being heated. The method for production of the α+β or β titanium alloy has a step of mixing 1 to 10 mass % of copper powder and the remainder of titanium alloy powder and a step of pressing and forming the mixture while being heated.