A process for producing a nano-structure is provided which enables control of the pore diameters and the pore intervals by film formation conditions. The process produces a nano-structure of an aluminum-silicon-germanium mixed film containing silicon and germanium at a content of 20 to 70 atom % relative to aluminum, the mixed film being constituted of a matrix composed mainly of silicon and germanium in a composition ratio of Si.sub.xGe.sub.1-x (0.ltoreq.X.ltoreq.1), and cylindrical portions mainly composed of aluminum having a diameter of not larger 30 nm in the matrix. In the process, the mixed film is formed at a film-forming rate of not higher than 150 nm/min.