Herein, we report the preparation and characterization of BaBi3 clarified by DC magnetic susceptibility, powder X-ray diffraction (XRD), and electrical transport. The superconducting properties of BaBi3 were elucidated through the magnetic and electrical transport properties in a wide pressure range. The superconducting transition temperature, Tc, showed a slight decrease (or almost constant Tc) against pressure up to 17.2 GPa. The values of the upper critical field, Hc2, at 0 K, were determined to be 1.27 T at 0 GPa and 3.11 T at 2.30 GPa, using the formula, because p-wave pairing appeared to occur for this material at both pressures, indicating the unconventionality of superconductivity. This result appears to be consistent with the topological non-trivial nature of superconductivity predicted theoretically. The pressure-dependent XRD patterns measured at 0-20.1 GPa indicated no structural phase transitions up to 20.1 GPa, i.e., the structural phase transitions from the α phase to the β or γ phase which are induced by an application of pressure were not observed, contrary to the previous report, demonstrating that the α phase is maintained over the entire pressure range. Admittedly, the lattice constants and the volume of the unit cell, V, steadily decrease with increasing pressure up to 20.1 GPa. In this study, the plots of Tcversus p and V versus p of BaBi3 are depicted over a wide pressure range for the first time.