Due to their extremely high specific energy, rechargeable Li-air batteries could meet the demand for large-scale storage systems to integrate renewable sources into the power grid. Li-air batteries with aqueous catholytes with high solubility of discharge products have a higher potential to reach their slightly lower theoretical limits in practical devices. In this work, we demonstrate aqueous and hybrid Li-air batteries with NASICON-type Li1+xAxGe2−x(PO4)3 ceramic as anode-protecting membrane. The LAGP ceramic pellets with room temperature conductivity >10−4 S cm−1 are synthesized by melt quenching and subsequently annealed based on our optimized heat treatment cycle. Hybrid Li-air batteries are assembled by sandwiching LAGP membranes between Li-anode chamber and catholyte solutions (of various pH values) with CNT/Pt as air-cathode. When the two electron reduction mechanism prevails, overpotentials below 0.2 V are achieved for currents up to 0.07 mA cm− 2 leading to energy efficiencies exceeding 98%.