The greenhouse effect has drawn significant recent attention due to its serious impact on Earth's climate and ecosystems. Therefore, this study investigates the adsorption and sensing properties of four greenhouse gases (CH4, CO2, SF6, and N2O) on the Ni-GeSe monolayer using first principles of DFT. The doping behavior of Ni on intrinsic GeSe monolayer is initially studied and the most stable doping structure is selected. Then the adsorption energies, adsorption distances, charge transfers, energy band structures, molecular frontier orbitals and recovery times of the selected Ni-GeSe structure with the four greenhouse gases are analyzed and compared. The results show that Ni modification can improve the surface activity of the intrinsic GeSe monolayers, thereby improving their adsorption and sensing properties. Ni-GeSe has weak adsorption of CH4 and CO2, while strong chemisorption of SF6 and N2O, making it suitable as an adsorbent for these two gases. Analysis of the recycling performance of Ni-GeSe monolayers shows that Ni-GeSe has a good recovery time for N2O at a temperature of 398K, suggesting its potential as an efficient low-power resistive N2O gas sensor. And gas sensors based on GeSe and its modified materials can be theoretically guided by these calculations.