Solid oxide fuel cells (SOFCs) have drawn remarkable attention in recent years due to their distinctive advantages of high efficiency, fuel variety and low environment pollution. Along the way to designing of new cathode materials for SOFCs, an understanding of the mechanism of oxygen reduction reaction (ORR) plays a key role, especially the interaction between O2 molecule and surface of cathode. The results of the first principles calculations of the atomic and electronic structure of a layered perovskite LaSrCo0.5Feo.5O4-δ used as a cathode material for solid oxide fuel cells (SOFCs) are presented and discussed. The oxygen vacancy formation energies is found to be smaller than LaSrCoO4 and slightly lower than the other perovskite, e.g. (La, Sr)MnO3, which widely used as a cathode because of its excellent catalytic activity. From a detailed analysis of difference electron densities, the presence of oxygen vacancies can induce local charge redistribution. Furthermore, a strong hybridization between Co-Oad and Fe-Oad for molecular adsorption was obtained by analysis of density of states. Our results show how the mixed B-site ions produce the excellent adsorption and conduction performance of LaSrCo0.5Feo.5O4-δ and fully support its potential application in next-generation SOFCs.