Li-oxygen batteries have attracted much attention in the last few years because of their relatively high theoretical energy densities compared to other batteries and because of the recent advancements in material technologies. The high theoretical energy density of Li-oxygen batteries makes these batteries suitable for applications requiring light power sources such as portable electronic devices, unmanned aerial vehicles, and renewable energy storage. In this presentation, we investigate the impact of the porosity distribution on the performance of Li-air batteries with cathodes made of carbon nanotube foams. After presenting the transport model appropriate for such cathodes, we develop a mathematical optimization method to find the optimum 1-D porosity distribution inside the Li-air battery that maximizes the energy density of these batteries. Our preliminary results show that to maximize the energy density of Li-air batteries, it is better to use cathodes with spatially variable porosity, in which the porosity at the oxygen entrance is higher than near the separator. More details about the mathematical approach and preliminary experimental data will be presented at the conference.