BaBiO3 is a well-known example of a 3D charge density wavecompound, in which the CDW behavior is induced by charge disproportionation at the Bi site. At ambient pressure, this compound is a charge-ordered insulator, but little is known about its high-pressure behavior. In this work, we study from first-principles the high-pressure phase diagram of BaBiO3 using phonon modes analysis and evolutionary crystal structure prediction. We show that charge disproportionation is very robust in this compound and persists up to 100 GPa. This causes the system to remain insulating up to the highest pressure we studied.