It is reported lithium superoxide as the discharge product can largely decrease the charge voltage and enable a high round-trip efficiency of lithium-oxygen (Li-O2) batteries. Here, we conduct a numerical investigation of the discharge behaviors of such batteries with LiO2 as the discharge product. A mathematical model considering the mass transport and electrochemical reaction processes is first developed, which gives good agreement of the simulated discharge voltage with the experimental data. Then, with this model, the effects of electrode and electrolyte properties on the discharge performance are detailedly investigated. It is found that a thin cathode with a large porosity is favorable for a high specific capacity, and a high catalytic activity can lead to a high discharge voltage. For the cathode with different geometrical properties, it is found that the oxygen solubility and diffusivity have similar impacts on discharge capacities, but the oxygen solubility has a larger impact on energy densities. Besides, the limitations and further developments of the present model are also discussed. The results obtained from this work may give useful guidance for the discharge performance improvements of non-aqueous Li-O2 batteries, and provide implications for other energy storage systems with solid product formation such as Na-O2 batteries and Li-S batteries.