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Compression behaviors of CaIrO with perovskite (Pv) and post-perovskite (pPv) structures have been investigated up to 31.0(1.0) and 35.3(1) GPa at room temperature, respectively, in a diamond-anvil cell with hydrostatic pressure media. CaIrO Pv and pPv phases were compressed with the axial compressibility of β > β > β and β > β > β, respectively and no phase transition was observed in both phases up to the highest pressure in the present study. The order of axial compressibility for pPv phase is consistent with the crystallographic consideration for layer structured materials and previous experimental results. On the other hand, Pv phase shows anomalous compression behavior in b axis, which exhibit constant or slightly expanded above 13 GPa, although the applied pressure remained hydrostatic. Volume difference between Pv and pPv phases was gradually decreased with increasing pressure and this is consistent with the results of theoretical study based on the ab initio calculation. Present results, combined with theoretical study, suggest that these complicate compression behaviors in CaIrO under high pressure might be caused by the partially filled electron of Ir. Special attention must be paid in case of using CaIrO as analog materials to MgSiO, although CaIrO exhibits interesting physical properties under high pressure. [ABSTRACT FROM AUTHOR]