We conducted a first-principles study on the electronic, magnetic, and optical characteristics of non-metallic atoms (B, C, F, H, N, O, P, S, and Si) doped in single-layer carbon germanium (GeC). The findings indicate that the introduction of various non-metallic atoms into the monolayer GeC leads to modifications in its band structure properties. Different non-metallic atoms doped in single-layer GeC will produce both magnetic and non-magnetic properties. B-, H-, N-, and P-doped GeC systems exhibit magnetic properties, while C-, F-, O-, S-, and Si-doped single-layer GeC systems exhibit non-magnetic properties. Different non-metallic-doped single-layer GeC systems will produce semiconductor, semimetallic, and metallic properties. The C-, N-, O-, P-, S-, and Si-doped GeC systems still exhibit semiconductor properties. The H-doped GeC system exhibits semimetallic properties, while the B- and F-doped GeC systems exhibit metallic properties. Other than that, the doping of B, H, N, and P atoms can modulate the magnetism of single-layer GeC. Subsequently, we studied the influence of the doping behavior on the work function, where the work function of the single-layer GeC system doped with P atoms is very small, indicating that its corresponding doping system (P-doped GeC system) can produce a good field emission effect. In the optical spectrum, the doped systems have a certain influence in the far ultraviolet region. Furthermore, our results showed that S- and Si-doped single-layer GeC systems are conducive to photocatalysis compared to the single-layer GeC system.