Two-dimensional (2D) semiconductor materials have emerged as one of the hotspots in recent years due to their potential applications in beyond-Moore technologies. In this work, we systematically investigate the electronic and optoelectronic properties of the g-GeC monolayer combined with strain engineering using first-principles calculations. The results show that g-GeC monolayer possesses a suitable direct bandgap and a strain-tunable electronic structure. On this basis, the designed g-GeC monolayer-based two-probe photodetector exhibits a robust broadband optical response in the visible and near-ultraviolet ranges, along with significant polarization sensitivity and high extinction ratio. In addition, strain engineering can greatly improve the optoelectronic performance of the g-GeC-based photodetector and effectively tune its detection range in the visible and near-ultraviolet regions. These findings not only deepen the comprehension of g-GeC nanosheet but also provide the possibility of its application in nano-optoelectronic devices.