A three-dimensional transient model is developed for a non-aqueous-electrolyte lithium-air battery to investigate numerically key phenomena during discharging. The proposed model rigorously assesses lithium peroxide (Li2O2) formation and growth in an air electrode, and its complex interactions with electrochemical reactions and species/charge transport. We assume that the porous air electrode mainly consists of sphere-like carbon particles, and hence a spherical film growth model is adopted to simulate the precipitation of Li2O2 on the spherical carbon surfaces. The model is first validated against voltage evolution data measured at different discharging current densities. Good agreement between the simulation results and experimental data is achieved, demonstrating that the model accurately captures voltage decline behaviors due to accumulated Li2O2 in the air electrode. Additional simulations are carried out with different air electrode designs in order to establish the optimization strategy for the air electrode. Detailed simulation results, including multidimensional contours, clearly indicate that the electrode thickness and degree of electrolyte filling are key factors for improving the discharging performance of lithium-air batteries.