Expensive Pt-based catalysts are usually required to achieve a high discharge voltage and long operation life for hybrid Li-air batteries. However, the cost of the catalysts needs to be lowered by either reducing the Pt loading in the catalysts or replacing Pt with less expensive catalysts. Here, we report the strong coupling of Co3O4 nanocrystals with an O- and N-doped carbon nanoweb (ON-CNW) as a low-cost, highly-efficient catalyst for hybrid Li-air batteries with an alkaline catholyte. Co3O4/ON-CNW greatly reduces the discharge overpotential compared to ON-CNW and exhibits longer cycle life, which is even better than that of the best reported N-doped mesoporous carbon (0.016% decrease in efficiency per cycle for 130 cycles compared to 0.017% decrease per cycle for 100 cycles obtained with N-doped mesoporous carbon). Although Pt/C exhibits a slightly higher initial discharge voltage (3.02V compared to 3.00V for Co3O4/ON-CNW), the cycle life of Pt/C is<50 cycles, making Co3O4/ON-CNW as a viable, stable cathode for hybrid Li-air batteries.