Metal−nitrogen carbon (M−N−C) catalysts, atomically dispersed and nitrogen-coordinated MN x sites embedded in carbon planes, have exhibited encouraging oxygen reduction reaction activity in an acidic environment. However, one challenge for these materials is their insufficient long-term stability in the acid environment. Herein, we systematically investigate both catalytic activity toward ORR and stability under acid conditions using density functional theory (DFT). Various local atomic structures around the MN x site and different metal atoms (M = Cr, Mn, Fe, Co, Ni, and Ru) are considered in this study to understand the relation between atomic structures, stability, and catalytic activity. The stability of the M−N−C catalyst is considered from the propensity of the metal atom center to dissolve from the carbon host structure. The calculations reveal that the considered MN x sites are thermodynamically unstable in acid ORR conditions. However, based on the calculated thermodynamic driving force toward the metal dissolution, the MN 4 sites with Fe, Co, Ni, and Ru metal atoms embedded on the graphene plane and at the graphene edge are more stable in the acid ORR condition than the other considered MN x structures. Combining the stability and catalytic activity descriptor, we propose some acid-stable and active MN x structures toward ORR. This computational study provides helpful guidance for the rational modification of the carbon matrix hosting MN x moieties and the appropriate selection of a metal atom for optimizing the activity and stability toward the ORR reaction.