A production method for a film having a fine asperity pattern on a surface thereof, wherein the roughness height of the fine asperity pattern is in the range of 10 nm to 1 mm and the film is composed of a thermoplastic resin as main component, said method comprising: (1-a) a film supply step in which a processing film taken out from a long film strip supply source provided on the upstream side is supplied intermittently with a predetermined length onto a mold surface having a fine asperity pattern, (1-b) a pattern forming step in which said processing film supplied onto said mold surface in said film supply step is pressed against said mold surface so that said pattern on said mold surface is transferred to a surface of said processing film to form a fine asperity pattern on the surface of said processing film, (1-c) a film peeling step in which a processed film having said pattern formed on its surface in said pattern forming step is peeled off from said mold surface, and (1-d) a film delivery step in which said processed film peeled off from said mold surface in said film peeling step is delivered to a long film strip storage source provided on the downstream side, thus processing a film in said pattern forming step to produce said processed film, peeling it off from said mold surface in said film peeling step, and then delivering said processed film to said film storage source in said film delivery step while another predetermined length of said processing film to be processed next is supplied intermittently onto said mold surface, in order to perform repeated production of said processed film with a predetermined length at a time, characterized in that (1-e) the peeling of said processed film in said film peeling step is achieved by a film holding means that holds said processed film and moves from the downstream side toward the upstream side in the length direction of said processed film, and (1-f) the supply of said processing film in said film supply step is achieved as a crease formation prevention means to prevent creases from forming on said processing film supplied onto said mold surface moves from the upstream side toward the downstream side in the length direction of said processed film. (1-a) a film supply step in which a processing film taken out from a long film strip supply source provided on the upstream side is supplied intermittently with a predetermined length onto a mold surface having a fine asperity pattern, (1-b) a pattern forming step in which said processing film supplied onto said mold surface in said film supply step is pressed against said mold surface so that said pattern on said mold surface is transferred to a surface of said processing film to form a fine asperity pattern on the surface of said processing film, (1-c) a film peeling step in which a processed film having said pattern formed on its surface in said pattern forming step is peeled off from said mold surface, and (1-d) a film delivery step in which said processed film peeled off from said mold surface in said film peeling step is delivered to a long film strip storage source provided on the downstream side, thus processing a film in said pattern forming step to produce said processed film, peeling it off from said mold surface in said film peeling step, and then delivering said processed film to said film storage source in said film delivery step while another predetermined length of said processing film to be processed next is supplied intermittently onto said mold surface, in order to perform repeated production of said processed film with a predetermined length at a time, characterized in that (1-e) the peeling of said processed film in said film peeling step is achieved by a film holding means that holds said processed film and moves from the downstream side toward the upstream side in the length direction of said processed film, and (1-f) the supply of said processing film in said film supply step is achieved as a crease formation prevention means to prevent creases from forming on said processing film supplied onto said mold surface moves from the upstream side toward the downstream side in the length direction of said processed film.