PURPOSE: To provide a coextruded multi-layer film which is suitable for materials for packaging or a file for stationery, etc., by a method wherein it is made to be free from curl and blocking, difficult to be injured, excellent in transparencey, excellent in shock strength, and heat seal strength, and has small aging with time.

CONSTITUTION: An outer layer is made of propylene, a core layer is composed of straight chain ethylene-α-olephin copolymer of 0.85 to 0.945g/cm3 in density, and a ratio of thickness of the outer layer, the core layer, and the outer layer is within a range of 10 to 45:80 to 10:10 to 45. Further, a straight chain ethylene-α-olefin copolymer of the core layer is individually or in a combined manner mixed with 0 to 40% of ethylene-acrylic acid copolymer, ethylene- methylacrylate copolymer, ethylene-methacrylic acid copolymer, ionomer, propylene homopolymer, and propylene-α-olefin copolymer, and melted materials of those three layers are quenched from the melted state of the polymer by using a cost method and a down blow water cooling inflation method to obtain the title film.