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Hydrogen peroxide is a radiolysis product of water formed under gamma-irradiation; therefore, its reliable detection is crucial in the nuclear industry for spent fuel management and coolant chemistry. This study proposes an electrochemical sensor for hydrogen peroxide detection. Cysteamine (CYST), gold nanoparticles (GNPs), and horseradish peroxidase (HRP) were used in the modification of a gold electrode for fabricating Au/CYST/GNP/HRP sensor. Each modification step of the electrode was investigated through electrochemical and physical methods. The sensor exhibited strong sensitivity and stability for the detection and measurement of hydrogen peroxide with a linear range of 1–9 mM. In addition, the Michaelis–Menten kinetic equation was applied to predict the reaction curve, and a quantitative method to define the dynamic range is suggested. The sensor is highly sensitive to H2O2 and can be applied as an electrochemical H2O2-sensor in the nuclear industry.