Laser drilling of engineering plastic films was performed using a picosecond pulsed laser at different repetition rates for the application of through-hole membranes to laser-drilled screen printing. Four engineering plastic films of polyimide (PI), poly(ethylene terephthalate) (PET), poly(phenylene sulfide) (PPS), and poly(ether ether ketone) (PEEK) were investigated. Frustum-shaped through holes were formed with high reproducibility by laser drilling at a repetition rate of 10 kHz. Higher repetition rates induced the formation of heat affected zone around the edge of the thorough holes in the case of engineering plastic films with their low melting point. The mean diameters of through holes formed on the film surfaces of both laser entry and exit sides at the identical repetition rate increased in the order of PEEK ≈ PET < PI < PPS, which had a relationship with the optical absorption properties at the wavelength of the laser pulses. It was suggested that the PI film was appropriate to a laser-drilled through-hole membrane in terms of the shape of through holes in addition to its chemical and thermal stabilities.