Hydrogen peroxide (H2O2) is a biomarker that indicates oxidative stress levels in the human body; thus, rapid and accurate detection methods are necessary to diagnose various disorders. This study developed a nonenzymatic electrochemical sensor for detecting H2O2 using bimetallic gold–silver nanoparticles (Au–Ag NPs) combined with graphene oxide and poly(3,4-ethylenedioxythiophene)-poly(styrenesulfonate)-modified glassy carbon electrode. The surface properties of the modified electrodes were characterized using scanning electron microscopy–energy dispersive spectroscopy and atomic force microscopy. The electrochemical performance of the modified electrodes was evaluated using cyclic voltammetry, electrochemical impedance spectroscopy, and differential pulse voltammetry. The bimetallic Au-Ag NP-modified electrodes exhibited a higher current response to H2O2 than their monometallic counterparts. The sensor demonstrated a linear response at the H2O2 concentration of 75–200 μM, with a sensitivity of 0.0407 μA μM⁻¹ and a detection limit of 25 μM. Moreover, the modified electrodes demonstrated excellent selectivity for H2O2 and high repeatability of measurements (relative standard deviation < 5%). The detection of H2O2 levels in synthetic urine samples yielded results that were not significantly different from those obtained by the spectrophotometry method, indicating the potential of the developed sensor for clinical applications.