It was established that the silver nanoparticles (AgNPs) in an equimolar ratio have the highest electrochemical activity on a graphite electrode (GE) surface in an alkaline medium. The electrocatalytic oxidation mechanism of hydrogen peroxide on the GE surface was proposed. We detected an additional maximum at E = 0.3 V on the cathodic branch of the cyclic curve in the potential range from +2.0 to -1.0 V. The appearance of this maximum indicates the reduction of hydrogen peroxide generated during AgNPs electrooxidation in the potential range from -1.0 to +2.0 V.