High energy density lithium-air batteries are ideal storage systems for future transportation like electric vehicles. The theoretical energy density of lithium-oxygen batteries is more than ten times greater than the energy density of lithium-ion batteries which are currently used in electric vehicles. In spite of high energy density of lithium oxygen batteries, there are several challenges that need to be overcome for development of these batteries. In the lithium-air batteries, oxygen crosses the separator to the anode/separator interface and reacts with the lithium anode known as oxygen crossover which is one the main challenges in lithium-air batteries. In the present study, this phenomenon, oxygen crossover, is investigated by Arrhenius equation for simulation of reaction kinetics. A mathematical model based on Newman porous electrode theory is implemented to simulate the cycling performance. The effect of diffusion coefficient, oxygen solubility, applied current density and oxygen crossover reaction kinetics parameter on the performance of the battery are investigated. The results show that with the reduction of diffusion coefficient and oxygen solubility in the electrolyte, the cycling performance is enhanced. But the increase in these two parameters leads to decay of efficiency and specific capacity. On the other hand, change in kinetics parameters have the same effects on the efficiency and cycling performance of the battery. Therefore, the key point in the performance enhancement is making barrier in the oxygen crossover reaction path.