Using first-principles calculations, we investigate the stability and electronic properties of five isomers of two-dimensional (2D) GeSe monolayer under in-plane strain. Our calculated results show that the five isomers of GeSe monolayer are all stable. It is found that the α-GeSe has a direct band gap, while each of the β-GeSe, γ-GeSe, δ-GeSe and ε-GeSe possesses an indirect band gap. By applying compressive or tensile uniaxial and biaxial strain to the five GeSe isomers, the indirect-to-direct transition in band gap is found. In the α-GeSe, the changes from indirect-to-direct and semiconducting-to-metallic are both found under an applied strain. In the 2D β-GeSe and γ-GeSe, an adjustable range of indirect band gap under strain is found. Moreover, a direct band gap in the δ-GeSe is found separately under the biaxial compression strain of σ _xy= –2% and σ _xy= –4%. By applying a tensile strain of 10% along the armchair direction in ε-GeSe, a transition from an indirect to direct band gap occurs. When the tensile strain is continuously increased to 20%, the band structure of ε-GeSe maintains direct character. This direct band gap can be tuned from 1.21 eV to 1.44 eV. When 10% tensile strain is applied along the biaxial direction, the transition in band gap from indirect-to-direct also occurs. Our results indicate that the direct band gap can be tuned from 0.61 eV to 1.19 eV when the tensile strain is increased from 10% to 19% in ε-GeSe.