Experimentally, GeS nanosheets have been successfully synthesized using vapor deposition processes and the one-pot strategy. Quite recently, GeS monolayer, the isoelectronic counterpart of phosphorene, has attracted much attention due to promising properties. By means of comprehensive first-principles calculations, we studied the stability and electronic properties of GeS monolayer. Especially, electric field and in-plane strain were used to tailor its electronic band gap. Upon applying electric field, the band gap of GeS monolayer greatly reduces and a semiconductor-metal transition happens under the application of a certain external electric field. Our calculations reveal that the band gaps of GeS monolayer are rather sensitive to the external electric field. On the other hand, for GeS under external strain, quite interestingly, we found that the band gap presents an approximately linear increase not only under compression strain but also under tensile strain from -10% to 10%. For biaxial compressive and tensile strains, the band gap follows the same trend as that of the uniaxial in the zigzag x direction. The present results provide a simple and effective route to tune the electronic properties of GeS monolayer over a wide range and also facilitate the design of GeS-based two-dimensional devices.