Herein, we provide critical information via first-principles calculations to solve one of the major problems of Li−O2 batteries, namely, large overpotentials during the charge–discharge process. First, we found that PtCo exhibits remarkably low oxygen reduction reaction (ORR) and oxygen evolution reaction (OER) overpotentials of 0.19 and 0.20V, respectively. These are considerably lower than those of pure Pt (1.02 and 1.62V, respectively) and of high-performance Pt3Co (1.02 and 1.13V, respectively). The composition optimization of bimetallic catalysts is therefore critical in developing an optimal Li−O2 battery catalyst with an overpotential of nearly zero. Second, our calculations demonstrate that replacing the late transition metal Co in Pt3Co with the early transition metal Ti significantly decreases overpotentials, yielding ORR and OER overpotentials of 0.34 and 0.82V, respectively. These results are opposite to those obtained for fuel cells. Notably, our results suggest that a bimetallic catalyst with poor catalytic activity in fuel cells might show excellent activity in Li−O2 cells. In particular, combinations of active Pt with early transition metals should be studied for development of bimetallic catalysts with high round-trip efficiency in Li−O2 batteries. Finally, we suggest that the adsorption energies of Li and LiO2 are critical descriptors of catalytic activity and that they should be used to screen new candidate materials. This is because low ORR and OER overpotentials are closely related to strong Li and weak LiO2 adsorptions, respectively, on the catalytic surface.