To access hydrogen peroxide scavenging activity, we propose a sensor based on core-shell iron-nickel hexacyanoferrate nanoparticles. On the one hand, the sensor preparation procedure is simple: syringing the nanoparticles suspension with subsequent annealing. On the other hand, the sensor demonstrates a stable response to 0.05 mM of H2O2 within one hour, which is sufficient for the evaluation of antioxidant activity (AO). The analytical performance characteristics of the sensor (0.5–0.6 A M−1 cm−2, detection limit 1.5 × 10−7 M and linear dynamic range 1–1000 µM) are leads to advantages over the sensor based on Prussian Blue films. The pseudo-first-order constant of hydrogen peroxide scavenging was chosen as a characteristic value of AO. The latter for trolox (standard antioxidant) was found to be linearly dependent on its concentration, thus allowing for the evaluation of antioxidant activity in trolox equivalents. The approach was validated by analyzing real beverage samples. Both the simplicity of sensor preparation and an expressiveness of analytical procedure would obviously provide a wide use of the proposed approach in the evaluation of antioxidant activity.