The structures and stabilities of alkaline earth metal peroxides XO₂ (X = Ca, Be, Mg) were studied using an adaptive genetic algorithm (GA) for global structure optimization in combination with first-principles calculations. From the adaptive GA search, we obtained an orthorhombic structure for CaO₂ with 12 atoms in the unit cell, which is energetically more favorable than the previously proposed structures. Reaction energy of the decomposition CaO₂ → CaO + 1/2O₂ determined by density functional theory (DFT) calculation shows that this orthorhombic calcium peroxide structure is thermodynamically stable. The simulated X-ray diffraction (XRD) pattern using our predicted structure is in excellent agreement with experimental data. We also show that crystal phase BeO₂ is unlikely to exist under normal conditions. MgO₂ has a cubic pyrite structure, but it is not stable against decomposition: MgO₂ → MgO + 1/2O₂.