We demonstrate a type of carbon nanotube based buckypaper cathode in a hybrid electrolyte Li-air battery (HyLAB) that showed outstanding discharging performances. The HyLAB has sulfuric acid as the catholyte and a large active electrode area (10cm2). The active cathode layer was made from a buckypaper with 5wt.% Pt supported on carbon nanotubes (Pt/CNTs) for oxygen reduction and evolution. A similar cathode was constructed with a catalyst of 5wt.% Pt supported on carbon black (Pt/CB). It is demonstrated that sulfuric acid can achieve high discharging current densities while maintaining relatively high cell potentials. The cell with Pt/CNTs showed a much better performance than with Pt/CB at high current densities. The HyLAB with Pt/CNTs achieved a discharging capacity of 306mAh/g and a cell voltage of 3.15V at 0.2mA/cm2. The corresponding specific energy is 1067Wh/kg based on the total weight of the sulfuric acid. Slow decrease in performance was observed, but it can be recovered by refilling the cell with new electrolyte after continuous discharging of more than 75h. A charge–discharge experiment at 0.2mA/cm2 showed that the cell was rechargeable with a capacity of more than 300mAh/g.