Strain engineering of perovskite quantum dots (pQDs) is widely studied with the advantage of tunable material properties in photonic devices. Here we investigated the structural phase transition and electronic properties of the situation where pressure was applied on one axis (z-axis). Using first-principle calculation, we can confirm under what conditions structural phase transitions occurs in this perovskite material when the pressure applied to perovskite is about 0.78 GPa. And at the room temperature, it was possible to describe the difference for the transition between the cubic phase and the orthorhombic phase of perovskite, which the experiment could not elaborate. In particular, we explained how the tilting of Pb-X-Pb and the bond length of Pb-X change as pressure is applied, how the valence band maximum (VBM) and conduction band minimum (CBM) shift, and how the phonon band and bonding characters are shown. Finding Gibbs free energy for cubic and orthorhombic phases using phonon was essential to determine the temperature dependence of phase transition. Since the cubic phase with high symmetry is stable in the high temperature, we proceeded with the calculation including the variation in the imaginary frequency for the high temperature. This study, which investigates the conditions for distinguishing the phase of CsPbBrI2 perovskite material, allows to adjust undesired phases when using an actual material, and can discuss the availability of new generation CsPbBrI2perovskite materials by adjusting bandgap and light emission frequencies.