Significant photoconductive effects are reported in emergent two-dimensional (2D) ${\mathrm{Bi}}_{2}{\mathrm{O}}_{2}\mathrm{Se}$. In this work, we investigate the layer-dependent photoresponse properties and photovoltaic effects of 2D ${\mathrm{Bi}}_{2}{\mathrm{O}}_{2}X$ (X = $\mathrm{S}$, $\mathrm{Se}$, and $\mathrm{Te}$) by first-principles calculations and quantum-transport simulation. The absorbance per layer increases with the decreasing layer number for high-frequency light, so the absorbance density of 2D ${\mathrm{Bi}}_{2}{\mathrm{O}}_{2}X$ can be elevated by decreasing the layer number. An outstanding open-circuit voltage (1.08 V) among 2D materials is found for the monolayer (ML) ${\mathrm{Bi}}_{2}{\mathrm{O}}_{2}\mathrm{Se}$ p-n junction. The computed responsivities of ML black phosphorous, ${\mathrm{Mo}\mathrm{S}}_{2}$, and ${\mathrm{W}\mathrm{Se}}_{2}$ p-n junctions through our methods are in good agreement with experiments. The ML ${\mathrm{Bi}}_{2}{\mathrm{O}}_{2}\mathrm{Se}$ and ${\mathrm{Bi}}_{2}{\mathrm{O}}_{2}\mathrm{Te}$ p-n junctions show responsivities of 16.8 and 13.6 mA/W, respectively, under AM1.5 sunlight; these values are higher than those of their extensively studied ML ${\mathrm{Mo}\mathrm{S}}_{2}$ (8.6) and ${\mathrm{W}\mathrm{Se}}_{2}$ (8.8) counterparts. The ${\mathrm{Bi}}_{2}{\mathrm{O}}_{2}\mathrm{Se}$ film and ${\mathrm{Bi}}_{2}{\mathrm{O}}_{2}\mathrm{S}$ p-n junctions also show higher responsivities than those of commercial $\mathrm{Si}$ and $\mathrm{Ga}\mathrm{As}$. Therefore, the 2D ${\mathrm{Bi}}_{2}{\mathrm{O}}_{2}X$ p-n junctions have prospective applications in photovoltaic devices.