In this study, electrospun polyacrylonitrile nanofibers were effectively functionalized for enhanced molybdenum ion adsorption through a multi-step approach. Initially, glycidyl methacrylate was grafted onto the nanofibers via irradiation-induced grafting polymerization, followed by chemical modification with various amino groups, with triethylamine identified as the optimal modifier. The impacts of key synthesis parameters and reaction conditions on grafting level and adsorption capacity were thoroughly investigated, with a focus on achieving maximum efficiency. The resulting nanofibers were characterized using FTIR, SEM, and BET techniques, confirming the successful modification and structural features conducive to adsorption. Furthermore, a comprehensive experimental design, incorporating a central composite design, yielded optimal conditions for molybdenum adsorption, with key parameters including monomer concentration, irradiation dose, adsorbent mass, initial concentration, time, pH, temperature, and amine concentration. The adsorption kinetics were effectively described by the pseudo-second-order model, while the Langmuir isotherm model provided valuable insight into the adsorption behavior. Impressively, the adsorbent exhibited exceptional adsorption efficiency, surpassing 98% even after six adsorption–desorption cycles using 0.5 M HCl. Thermodynamic analysis revealed the exothermic nature of the adsorption process, along with decreased entropy and overall spontaneity, underlining the favorable conditions for molybdenum adsorption. Notably, the synthesized adsorbent demonstrated notable selectivity for molybdenum and achieved an impressive adsorption capacity of 109.79 mg/g, highlighting its potential for practical applications in molybdenum removal from aqueous solutions.