Research has been devoted to the desalination of saline water to fresh water suitable for human demands because of the shortage of water in some countries. Therefore, in this study, reverse-osmosis membranes were prepared via the g-radiation graft copolymerization of acrylic acid onto high-density and low-density polyethylene. The factors that could affect the grafting process, such as the solvent type, monomer and inhibitor concentration, and irradiation dose, were investigated to determine the optimum conditions for radiation grafting. The polyethylene grafted acrylic acid copolymers (PAAc-g-PE) graft copolymer was characterized by Fourier transform infrared spectroscopy, scanning electron microscopy, and mechanical, rheological, and thermal property testing to illustrate the possibility of practical use in water desalination. The prepared grafted membranes showed significant results in the reverse-osmosis desalination method with underground saline water. The factors affecting the desalination of water, such as the water flux, operation time, and grafting percentage, were studied.