A novel process for the production of a separator for use in a cell to prevent the short-circuiting of positive active material and negative active material comprises irradiating a polyolefin film 150 .mu.m or less thick with ionizing radiation at a dose rate of 5.times.10.sup.4 -10.sup.7 rads/sec. to give a total dose of 1 Mrad or more, contacting the irradiated film with an aqueous solution of a terminally unsaturated monomer such as acrylic acid, methacrylic acid and the like at a temperature of 10.degree. C.-60.degree. C. to thereby cause grafting of the monomer onto the polyolefin film before the grafted polymer film is treated with an aqueous alkaline solution to finally obtain the separator for use in a cell, which is substantially improved in that it shows low electrical resistance and is excellent both in its acid resistance and mechanical strength.