We performed high-pressure study for a Mott insulator BaFe_{2}S_{3}, by measuring dc resistivity and ac susceptibility up to 15 GPa. We found that the antiferromagnetic insulating state at the ambient pressure is transformed into a metallic state at the critical pressure, P_{c}=10 GPa, and the superconductivity with the optimum T_{c}=24 K emerges above P_{c}. Furthermore, we found that the metal-insulator transition (Mott transition) boundary terminates at a critical point around 10 GPa and 75 K. The obtained pressure-temperature (P-T) phase diagram is similar to those of the organic and fullerene compounds; namely, BaFe_{2}S_{3} is the first inorganic superconductor in the vicinity of bandwidth control type Mott transition.