The structural, bonding, and dynamic properties of liquid boron oxide, B2O3, under pressure are studied by ab initio molecular-dynamics simulations. To investigate the pressure dependence of the static structure, we obtain the structure factors, the pair distribution functions, and the distribution of the coordination numbers as a function of pressure. Planar BO3 units are hardly deformed under pressures up to about 3 GPa, and the number of tetrahedral BO4 units increases gradually under further compression. The bond-overlap populations and the Mulliken charges as well as the electronic density of states show that the covalent character is well preserved in the liquid state up to at least 200 GPa, although bond weakening occurs due to the increase in the coordination number. When the temperature is relatively low, the self-diffusion coefficients of boron and oxygen have a maximum at about 10 GPa because the concerted reactions, which enhance the atomic diffusion, occur more frequently with the increase in pressure below 10 GPa and are suppressed at higher pressures. The maximum behavior of the diffusivity becomes weaker with increasing temperature. A remarkable feature of the dynamic properties is that, under higher pressures over 20 GPa, the diffusivity of oxygen becomes much smaller than that of boron, regardless of temperature, while the former is slightly larger than the latter at lower pressures. Detailed discussions on the microscopic origin of this anomalous pressure dependence of the diffusivity are given.