A method of manufacturing a high-purity refractory metal or a an alloy based thereon, said refractory metal being selected from the group consisting of niobium, rhenium, tantalum, molybdenum, and tungsten, comprising the steps of compacting a mixed material, in the form of powders or small lumps, of a refractory metal or alloy to be refined together with one or two or more additive elements selected from the group of transition metal elements consisting of vanadium, chromium, manganese, iron, cobalt and nickel, and from the group of rare earth elements, sintering the resulting compact at a high temperature of at least 1000.degree. C. and a high pressure of at least 100 MPa, thereby forming a lower compound or nonstoichiometric compound between at least a part of the additive element or elements and the impurity gas ingredient element such as O, N, C, and H, contained in the refractory metal or alloy to be refined, and thereafter electron-beam melting the sintered body. The material's functions (superconductivity, corrosion resistance, high temperature resistance, etc.) and workability (forging, rolling, and cutting properties) are markedly improved.