Evolutionary algorithms and density functional theory are applied to investigate the Ge–Se system under pressure. Binary crystalline compounds Ge₂Se₃ and Ge₃Se₄ with unconventional stoichiometries are predicted to be energetically and dynamically stable. Ge₂Se₃ with a space group of R3m(hR5) is predicted to become stable above 5 GPa and exhibit phase transitions at higher pressures. Ge₃Se₄ is found to become stable from 40 GPa with a body-centred cubic I3d crystal structure. Moreover, the conventional GeSe compound is predicted to become unstable above 50 GPa. By calculating the electron localization function, we show that electrons become more delocalized in Ge₂Se₃ as pressure increases. On the basis of band structure and electron–phonon coupling computations, Ge₂Se₃ and Ge₃Se₄ are shown to be metallic and exhibit superconducting transitions at low temperatures.