Using first-principles calculations based on density functional theory, we investigate the electronic structures and optical properties of germanium doped by phosphorus and bismuth with different concentrations. By analyzing the electronic structures and optical properties of the doped systems, we can theoretically analyze and predict the optical and electrical practical applications of N-doped germanium semiconductors. By analyzing and comparing the densities of electronic states before and after doped, we can draw some conclusions. The conclusions show that the Fermi level moves in the direction of conduction band after being doped. Although germanium is an indirect band gap luminescent material, the doped systems all become direct band gap luminescence. Doping more or less affects various optical properties in different energy ranges. In a low energy range, the dielectric function and refractive index of the doped systems are affected. When the doping concentration is 2.083%, the dielectric function and refractive index of the doped system both have a special change. And the absorption of the doped system is changed in the high energy. As the energy increases after the absorption peak, the absorption of the doped system drops faster. The reflectance of the doped system is affected in all the energy ranges. The reflectance of the doped system increases in medium energy. And the reflectance of the doped system is reduced in low energy and high energy range. However, when the doping concentration is 2.083% and the energy is less than 1.7 eV, the reflectance of the doped system is higher than that of the undoped system. The conductivity of the doped system forms two peaks, adding a peak in low energy. The additional peaks in the systems where the doping concentrations are 1.563% and 2.083% are obvious. The peak of the loss function increases after being doped. However, as the doping concentration increases, the increment of the loss function decreases. As the doping concentration increases, the peak is formed at a higher energy. The conclusions are of significance for guiding the optical applications of N-type doped germanium. According to the conclusions, we can adjust the doping concentration and energy range in the optical applications of N-doped germanium.