There is provided a method for continuous production of a functional membrane whereby a functional membrane in which a functional polymer is filled into the micropores of a porous resin sheet can be obtained both continuously and efficiently.The method for continuous production of a functional membrane of the present invention comprises a step for impregnating and depositing a polymer precursor having a functional group on a continuously conveyed porous resin sheet; a polymerization step for continuously feeding and bringing into contact first and second resin films to one side and the other side, respectively, of the precursor-impregnated/deposited sheet comprising the porous resin sheet into which the polymer precursor is impregnated and deposited, and polymerizing the polymer precursor in a state in which the sheet is sandwiched between the two resin films; a film peeling step; and a polymer removal step.