Motivated by the recent realization of two-dimensional (2D) nanomaterials as gas sensors, we have investigated the adsorption of gas molecules (SO₂, NO₂, HCN, NH₃, H₂S, CO, NO, O₂, H₂, CO₂, and H₂O) on the graphitic GaN sheet (PL-GaN) using density functional theory calculations. It is found that among these gases, only SO₂ and NH₃ gas molecules are chemisorbed on the PL-GaN sheet with apparent charge transfer and reasonable adsorption energies. The electronic properties (especially the electric conductivity) of the PL-GaN sheet showed dramatic changes after the adsorption of NH₃ and SO₂ molecules. However, the strong adsorption of SO₂ on the PL-GaN sheet makes desorption difficult, which precludes its application to SO₂ sensors. Therefore, the PL-GaN sheet should be a highly sensitive and selective NH₃ sensor with short recovery time. Furthermore, the adsorption of NO (or NO₂) molecules introduces spin polarization in the PL-GaN sheet with a magnetic moment of about 1 μ_B, indicating that magnetic properties of the PL-GaN sheet are changed obviously. Based on the change of magnetic properties of the PL-GaN sheet before and after molecule adsorption, the PL-GaN sheet could be used as a highly selective magnetic gas sensor for NO and NO₂ detection.