The two major classes of unconventional superconductors, cuprates and Fe-based superconductors, have magnetic parent compounds, are layered, and generally feature square-lattice symmetry. We report the discovery of pressure-induced superconductivity in a nonmagnetic and wide band gap 1.95 eV semiconductor, Cu2I2Se6, with a unique anisotropic structure composed of two types of distinct molecules: Se-6 rings and Cu2I2 dimers, which are linked in a three-dimensional framework. Cu2I2Se6 exhibits a concurrent pressure-induced metallization and superconductivity at similar to 21.0 GPa with critical temperature (T-c) of similar to 2.8 K. The T-c monotonically increases within the range of our study reaching similar to 9.0 K around 41.0 GPa. These observations coincide with unprecedented chair-to-planar conformational changes of Se-6 rings, an abrupt decrease along the c-axis, and negative compression within the ab plane during the phase transition. DFT calculations demonstrate that the flattened Se-6 rings within the CuSe layer create a high density of states at the Fermi level. The unique structural features of Cu2I2Se6 imply that superconductivity may emerge in anisotropic Cu-containing materials without square-lattice geometry and magnetic order in the parent compound.