It has been widely believed that SrO2, a typical alkaline earth metal peroxide, should adopt the tetrahedral CaC2-type structure (space group 14/mmm) at ambient pressure. Here we report a monoclinic structure (space group C2c), as predicted from first principles swarth structure searching simulations, is energetically more" favorable than the CaC2-type structure at ambient pressure- and low temperature, While the ILF/mmm structure is only stable at pressure (>20 GPa), elevated temperature conditions. A key, difference between these structures is the distinct 'orientation of peroxide ions. Especially, frozen-phonon -calculations indicate that the C2c structure can be derived by a softening 'Mode phonon:from I4/ romm structure. Furthermore, a high-pressure phase of SrO2, with P21/c symmetries containing two, layers of peroxide, ions with different orientations is uncovered at pressures higher 'than 36 GPa. Our electronic band calculations indicate that all the stable structures' of SrO2 are wide band gap semiconductors. Our results, represent a step forward toward a more complete understanding of the, structures and properties of alkaline earth metal peroxides.