The development of high-performance gas sensing materials is one of the development trends of new gas sensor technology. In this work, in order to predict the gas-sensitive characteristics of HfSe₂ and its potential as a gas-sensitive material, the interactions of nonmetallic element (O, S, Te) doped HfSe₂ monolayer and small molecules (NH₃ and O₃) have been studied by first-principles based on density functional theory. The results show that the adsorption of NH₃ and O₃ on pristine HfSe₂ monolayer is weak, and the adsorption strength can be significantly improved by doping O. And O-HfSe₂ is chemical adsorption to O₃ with large adsorption energy and transfer charge, and the band gap of O[sbnd]HfSe₂ disappears after adsorbing O₃, indicating that the adsorption of O₃ has a significant effect on the electrical properties of the substrate. These mean that O₃ is difficult to recover from the substrate surface, thus preventing O-HfSe₂ from developing into a sensitive material for O₃ detection. After doping S, the charge transfers and adsorption strength to NH₃ are the largest, but it is still small. So, the strain effect on the S-HfSe₂/NH₃ adsorption system is also studied. The results indicate that the adsorption strength of S-HfSe₂ to NH₃ can be enhanced by stretching S-HfSe₂ along x-axis. After absorbing NH₃, the conductivity of x-axis strained S-HfSe₂ changes, which suggest its sensitivity. And the predicted recovery times of S-HfSe₂ surfaces with ε_x=4%, 6% and 8% are 0.027 s, 1.153 s and 102.467 s, respectively, which suggests that the S-HfSe₂ monolayer has the potential to be developed as a sensitive material for NH₃ detection. These adsorption mechanism studies can also serve as a theoretical foundation for the experimental design of gas-sensing materials.