Based on the first-principles calculations of density functional theory, the stability, electronic structure, and optical properties of single layer GeC, N-doped, As doped, and N-As doped GeC systems were systematically studied. The results show that the single layer GeC is a direct bandgap semiconductor with the bandgap of 2.10 eV. Compared with the single layer GeC, the bandgap and work function of the doped system decrease, indicating that the required energy for electronic transition is relatively small in our doped system. Moreover, the light absorption coefficient of the doped system improves, and the absorption band edge has also undergone a red shift, effectively expanding the response range of the system to light and improving the absorption ability of the system to photons. In addition, the As doped GeC system not only exhibits impurity levels near the Fermi level, but also shows the optimal optical properties such as absorption coefficient, static dielectric function, and extinction coefficient in the low energy region. The above research can provide a theoretical basis for the preparation of relevant GeC photoelectric experiments.