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A computational investigation over structural and electronic properties of perovskite compound namely LaAlO3 using WIEN2K code by means of Full-potential (FP) Linearized Augmented Plane Wave (LAPW) method using DFT (Density Functional Theory) have been analyzed under the effect of pressure to brief the trend of phase transition in the present compound. The compound is investigated up to the pressure of 9.068 GPa from the ambient condition. In this study, the cubic structural properties of the proposed compound are analyzed under pressure and initiated with a = 7.2108 bohr belonging to cubic primitive and 1000 K points with RMT_ KMax is 7. From the analysis of Density of state (DoS) histograms profiles, it evidently shows that the compound being an insulator by the increment in the band gap under the applied pressure. The structural phase transition occurs at the pressure value 6.318 GPa and compression of volume 15 % from the ambient condition. In this range of pressure, a closedcontour occurs around La to Al and La to O atoms, It depicts that the formation of covalent bond between the mentioned atoms, may increase the stability of the compound.