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Alkaline-earth metal oxides, in particular MgO and CaO dominate Earths lower mantle, therefore, exploring high pressure behavior of this class of compounds is of significant geophysical research interest. Among all these compounds, BaO exhibits rich polymorphism in the pressure range of 0-1.5 Mbar. Static enthalpy calculations revealed that BaO undergoes a pressure induced structural phase transition from NaCl-type (B1) $\rightarrow$ NiAs-type (B8) $\rightarrow$ distorted CsCl-type (d-B2) $\rightarrow$ CsCl-type (B2) at 5.1, 19.5, 120 GPa respectively. B1 $\rightarrow$ B8 $\&$ B8 $\rightarrow$ d-B2 transitions are found to be first order in nature whereas d-B2$\rightarrow$ B2 is a second order or weak first order phase transition. Interestingly, d-B2 phase shows stability over a wide pressure range, $\sim$19.5-113 GPa. Mechanical and dynamical stabilities of ambient and high pressure phases are demonstrated through computed elastic constants and phonon dispersion curves, respectively. Under high pressure, significant phonon softening and soft phonon mode along M-direction are observed for B8, d-B2 and B2 phases, respectively. Pressure dependent Raman spectra suggest a phase transition from d-B2 to Raman inactive phase under pressure. Overall, the present study provides a comprehensive understanding of underlying mechanisms behind pressure-induced structural phase transitions in BaO.