This paper presents research on the technological development of hydrogen-air fuel cells with high output power characteristics using fluorine-free co-polynaphtoyleneimide (co-PNIS) membranes. It is found that the optimal operating temperature of a fuel cell based on a co-PNIS membrane with the hydrophilic/hydrophobic blocks = 70/30 composition is in the range of 60–65 °C. The maximum output power of a membrane-electrode assembly (MEA), created according to the developed technology, is 535 mW/cm2, and the working power (at the cell voltage of 0.6 V) is 415 mW/cm2. A comparison with similar characteristics of MEAs based on a commercial Nafion 212 membrane shows that the values of operating performance are almost the same, and the maximum MEA output power of a fluorine-free membrane is only ~20% lower. It was concluded that the developed technology allows one to create competitive fuel cells based on a fluorine-free, cost-effective co-polynaphthoyleneimide membrane.