To provide a method for immobilizing an alkane-oxidizing enzyme capable of efficiently immobilizing the enzyme, improving its heat-stability and utilizing it for production of alcohol by immobilizing the alkane-oxidizing enzyme to a high specific surface substrate.

This method comprises immobilizing an alkane-oxidizing agent of e.g. an enzyme produced by thermophilic alkane-assimilating bacteria to an electroconductive high specific surface substrate of e.g. oxygen-permeable membrane or carbonaceous substance by using a non-bonding immobilization selected from the group consisting of a gel immobilization method, micell immobilization method, electrolytic polymerization method and adsorption immobilization method applicable to high specific surface. This enzyme immobilization pref. comprises immobilizing enzymes, including methane monooxygenases(MMO) and methanol hydrogenase(MDH), allowed to be produced by alkane-assimilating bacteria to a substrate, and methanol is pref. produced by feeding methane to a bioreactor containing the immobilized enzymes.