We have studied the effect of hydrostatic pressure on the superconducting and normal state properties of non-centro symmetric (NCS) superconductor Re5.5Ta using magneto transport, magnetization and band structure studies. The superconducting transition temperature (T_c) reveals a modest decrease of ~ 0.52 K as the external pressure raised to 8 GPa. We found that the Maki parameter, αM>1, both at ambient and high pressure suggests the significant role of Pauli pair breaking effect. Furthermore, the lower critical field was found to be decreased with the rate of -1.74 mT/GPa as pressure increases to 1.05 GPa. The analysis of thermally activated flux flow region of ρ(T,H) by Arrhenius equation reveals the coexistence of single and collective vortex states. Further analysis of critical current density indicates that the surface and volume pinning center coexist and remain unaffected with varying pressure. The band structure calculations were done using density functional theory reveals a large bulk modulus, B0~ 289 GPa with B0
' ~ 3.7 suggesting poor compressibility. In addition, we found that the density of states at the Fermi level reduces barely even up to 20 GPa, consistent with the experimental observation of robust superconductivity under compression.