The present invention relates to a method of methane steam reforming using a nickel/alumina nanocomposite catalyst. More specifically, the present invention relates to a method of carrying out methane steam reforming using a nickel/alumina nanocomposite catalyst wherein nickel metal nanoparticles are uniformly loaded in a high amount on a support via a melt infiltration method with an excellent methane conversion even under a relatively severe reaction condition of a high gas hourly space velocity or low steam supply, and to a catalyst for this method. In addition, the present invention prepares a nickel/silica-alumina hybrid nanocatalyst by mixing the catalyst prepared by the melt infiltration method as the first catalyst and the nickel silica yolk-shell catalyst as the second catalyst, and applies it to the steam reforming of methane to provide a still more excellent catalytic activity even under the higher temperature of 700° C. or more with the excellent methane conversion.