Utilizing first-principles calculations, the structural, electronic and optical properties of two-dimensional germanium selenide (GeSe) with puckered and buckled structures are investigated. The electronic properties investigations reveal that the buckled GeSe monolayer has an indirect band gap of 2.38 eV and the puckered GeSe monolayer has a direct band gap of 1.15 eV. Applying biaxial strain significantly alters the electronic properties of the puckered and buckled GeSe monolayers. In the buckled GeSe monolayer, the band gap decreases by applying tensile or compressive strain, but for the puckered GeSe monolayer, it becomes zero for − 6% strain and increases to 1.49 eV when strain increases to + 6%. In the presence of the compressive strain and −6% strain, the puckered GeSe structure shows direct to indirect band gap and semiconductor to metal transitions, respectively. Both materials show a wide range of light absorption covering some part of the visible spectrum.