In this study, we present the structural and electronic bandgap properties of anatase and rutile titanium dioxide by applying ultrasoft pseudo-potential plane wave approach developed within the frame of density functional theory (DFT). We used generalized gradient approximation (GGA) proposed by Perdew-Burke-Ernzerhof (PBE) for exchange correlation potential. In our pressure driven investigations, geometry optimization is carried out for different values of pressure over a range of 0-100 GPa and subsequently related structural parameters and bandgap values of anatase and rutile titanium dioxide (TiO2) have been calculated. In both cases, the lattice constants (a, c) and volume decreased as the pressure was increased. Similarly, internal parameter for anatase increased and for rutile TiO2 it decreased under high pressure. The value of c/a decreased for anatase and increased for rutile TiO2 as a function of pressure. Our band structure analysis showed different behavior of bandgap between anatase and rutile TiO2. The conduction band of anatase TiO2 moved opposite to the conduction band of rutile TiO2 as we increased the pressure. Additionally we used the Birch-Murnaghan equation of state to obtain the equilibrium volume (V0), bulk modulus (B0) and pressure derivative of bulk modulus (B0’) at zero pressure. The calculated results are in good agreement with previous experimental as well as theoretical results.