All the iron-based superconductors identified so far share a square lattice composed of Fe atoms as a common feature, despite having different crystal structures. In copper-based materials, the superconducting phase emerges not only in square-lattice structures but also in ladder structures. Yet iron-based superconductors without a square-lattice motif have not been found, despite being actively sought out. Here, we report the discovery of pressure-induced superconductivity in the iron-based spin-ladder material BaFe2S3, a Mott insulator with striped-type magnetic ordering below similar to 120 K. On the application of pressure this compound exhibits a metal-insulator transition at about 11 GPa, followed by the appearance of superconductivity below T-c = 14 K, right after the onset of the metallic phase. Our findings indicate that iron-based ladder compounds represent promising material platforms, in particular for studying the fundamentals of iron-based superconductivity.