Layered hexagonal γ-GeSe, a new polymorph of germanium selenide (GeSe) synthesized recently, shows strikingly high electronic conductivity in its bulk form (even higher than graphite) while semiconducting in the case of monolayer (1L). In this work, by using first-principles calculations, we demonstrate that, different from its orthorhombic phases of GeSe, the γ-GeSe shows a small spatial anisotropic dependence and a strikingly thickness-dependent behavior with transition from semimetal (bulk, 0.04 eV) to semiconductor (1L, 0.99 eV), and this dual conducting characteristic realized simply with thickness control in γ-GeSe has not been found in other two-dimensional materials before. The lacking of d-orbital allows charge carrier with small effective mass (0.16 m for electron and 0.23 m for hole) which is comparable to phosphorene. Meanwhile, 1L γ-GeSe shows a superior flexibility with Young’s modulus of 86.59 N m, only one-quarter of that of graphene and three-quarters of that of MoS, and Poisson’s ratio of 0.26, suggesting a highly flexible lattice. Interestingly, 1L γ-GeSe shows an in-plane isotropic elastic modulus inherent with hexagonal symmetry while an anisotropic in-plane effective mass owing to shifted valleys around the band edges. We demonstrate the feasibility of strain engineering in inducing indirect-direct and semiconductor-metal transitions resulting from competing bands at the band edges. Our work shows that the free 1L γ-GeSe shows a strong light absorption (∼10 cm) and an indirect bandgap with rich valleys at band edges, enabling high carrier concentration and a low rate of direct electron-hole recombination which would be promising for nanoelectronics and solar cell applications.