Uranyl ions in seawater are prone to complexing with organic matter, forming stable compounds that can impact the adsorption performance of uranium adsorption materials. Herein, glycidyl methacrylate (GMA) monomers were introduced onto the surface of the polypropylene/polyethylene nonwoven (PP/PE SNW) substract using radiation-induced graft polymerization (RIGP). Thereafter, three different polyamines, namely, triethylenetetramine (TETA), tetraethylenepentamine (TEPA), and pentaethylenehexamine (PEHA), were utilized to a ring-opening reaction, introducing the amine group into the substrate. This was followed by an addition reaction with acrylonitrile and an amidoxime reaction to produce the straight-chain-structured AO-based adsorbents, termed P-TETA-AO, P-TEPA-AO, and P-PEHA-AO. Subsequently, structural characterization, adsorption performance investigation, and adsorption mechanism analysis were performed. The experimental results confirm that three different functional polymer chains with varying chain lengths were successfully modified on the substrate surface and that the target amidoxime-based adsorption material was successfully prepared. The adsorption process followed a pseudo-second-order kinetic model, and the adsorption isotherm was well described by the Langmuir model. The adsorption capacities of P-TETA-AO, P-TEPA-AO, and P-PEHA-AO for uranium were 66.1 mg/g, 63.22 mg/g, and 65.62 mg/g, respectively, within 24 h and exhibited adequate adsorption performance in the pH range of 5~9. The adsorption-desorption experiments indicated good regenerability, with only a 6% decrease in the uranium adsorption rate after five cycles, and a desorption ratio that was consistently above 95%. In the simulated seawater adsorption experiment, the uranium removal rates for P-TETA-AO, P-TEPA-AO, and P-PEHA-AO were found to be 72.94%, 79.97%, and 87.78%, respectively, indicating that the adsorption performance improved with the growth of the grafting chain in a highly saline, multi-competitive ion environment. The X-ray photoelectron spectroscopy results indicate that during uranium adsorption, the amino and amidoxime groups of all three adsorption materials participate in the coordination with uranyl ions, demonstrating a synergistic effect.