Two-dimensional ferroelectric materials have emerged as a promising candidate for the development of next-generation photodetectors owing to their inherent photogalvanic effect (PGE) and strong light-matter interactions. Recently, the first-ever elemental-based ferroelectric material, black-phosphorus-like Bi (BP-Bi), has been successfully synthesized. In this work, we investigate the PGE of the monolayer (ML) BP-Bi by using ab initio quantum transport simulation. We find that the photocurrent of the ML BP-Bi in the ferroelectric direction (armchair) is significantly larger than that in the vertical ferroelectric direction [zigzag (ZZ)]. For example, despite the comparable optical absorption rates of BP-Bi in the armchair (ARM) and ZZ directions, the maximum photocurrent (133 mA/W) in the ARM direction is 2 orders of magnitude greater than that (4.70 mA/W) in the ZZ direction. The asymmetry is attributed to the breaking and existence of the mirror inversion symmetries along the ARM and ZZ directions, respectively. Our work paves the way for the research of the low-dimensional ferroelectric photodetector.