Solid-state lithium–air cells using lithium anode, a polymer electrolyte, Li1+x+yAlx(Ti, Ge)2−xSiyP3−yO12 inorganic solid electrolyte, and an air electrode composed of carbon nanotubes and an inorganic solid electrolyte are constructed and their electrochemical properties investigated. The cells show a reversible capacity of about 400 mA h g−1 during the first few cycles. The rate performance and impedance measurements are also examined. The large cell resistance, which mainly comes from the interfacial resistance between Li and the polymer electrolyte, limits the rate performance. The results indicate that such all-solid-state lithium–air batteries without polymer electrolytes have good potential for development.