The production of effective catalysts in the oxygen reduction reaction (ORR) continues to be a great challenge for scientists. A constant increase in demand for energy storage materials is followed by a proportionate increase in the number of reports on electrocatalyst synthesis. The scientific world focuses on environmentally friendly materials synthesized in accordance with the safest possible. In this work, we developed a facile method of obtaining heavy-metal-free electrode materials that are effective in ORR. Graphene-based catalysts were doped using azodicarbonamide (ADC) as the source of nitrogen, then carbonized at high temperatures in the range of 700-900 °C under inert gas flow. The produced materials were tested as catalysts for ORR, which is the most important reaction for Zn-air batteries and fuel cells. All obtained nitrogen-doped graphene foams showed increased catalytic activity in ORR owing to active sites created by nitrogen functional groups on the graphene surface. This paper shows that carbonization temperature has a significant impact on nitrogen content and that a small percentage of nitrogen may have a positive effect on the catalytic activity of the obtained materials. The number of transferred electrons in ORR was found to range from three to the maximal theoretical value, i.e., four.