Ferroelectric materials are promising candidates for ultraviolet photodetectors due to their ferroelectric effect. In this work, a BaTiO3/p-GaN/Au hybrid heterojunction-Schottky self-driven ultraviolet photodetector was fabricated with excellent bipolar photoresponse property. At 0 V bias, the direction of the photocurrent can be switched by flipping the depolarization field of BaTiO3, which allows the performance of photodetectors to be controlled by the ferroelectric effect. Meanwhile, a relatively large responsivity and a fast response speed can be also observed. In particular, when the depolarization field of BaTiO3 is in the same direction as the built-in electric field of Au/p-GaN Schottky junction (up polarized state), the photodetector exhibits a high responsivity of 18 mA/W at 360 nm, and a fast response speed of <40 ms at 0 V. These findings pave a new way for the preparation of high-performance photodetectors with bipolar photocurrents.