This study developed flexible textile biosensors based on rGO/Ag nanocomposite to detect adrenaline (epinephrine). Reduced graphene oxide (rGO) and Ag nanoparticles (NPs) were obtained in a single step using the electron-beam irradiation technique, a rapid, efficient, plain, ecofriendly, and easily scalable procedure. The nanocomposites’ properties were characterized by ultraviolet–visible-light spectroscopy, Fourier-transform infrared spectroscopy, scanning electron microscopy, cyclic voltammetry, and electrochemical impedance spectroscopy. Furthermore, the obtained sensors’ electrochemical behaviors of epinephrine were investigated using square wave voltammetry (SWV), linear sweep voltammetry, and differential pulse voltammetry methods. The optimum experimental conditions included pH 7, phosphate borate buffer, accumulation time of 100 s, accumulation potential of 0.4 V, and a scan rate of 100mV/s. In addition, the anodic peak currents of epinephrine by SWV were 16.33 and 13.9 µA for rGO/AgNP/cotton and rGO/AgNP/polyester, respectively. The fabricated flexible textile biosensors exhibited high sensitivity and strong catalytic activity for epinephrine detection. Under optimal testing conditions, in the range of 0.5–100.0 µL, two detection lines and a low limit of detection (LOD) of 9.73 nM (S/N = 3) for epinephrine were obtained for cotton and polyester biosensors. Two wide detection ranges were observed at 0.5–40.0 µL for cotton biosensors, whereas there was a lower LOD of 3.05 nM (S/N = 3) at 1.0–30 µL for polyester biosensors. Overall, the constructed electrode can serve as a promising analytical sensor for adrenaline determination in pharmaceutical and biological samples.