[en] As a potential red-light source in the white light emitting diodes (LEDs), Mn-doped magnesium fluorogermanate (Mg₂₈Ge_7.5O₃₈F₁₀) are investigated by the first principles calculation with the Heyd-Scuseria-Ernzerhof (HSE) functional. The results demonstrate that the neutral Mn substitutions at the Mg (Mn${}_{\text{Mg}}$), octahedral Ge (Mn${}_{\text{Ge}\left(\text{oct}\right)}$) and tetrahedral Ge (Mn${}_{\text{Ge}\left(\text{tet}\right)}$) sites are all energetically favorable. However, only Mn${}_{\text{Mg}}$ could create proper transition levels leading to the experimentally observed red-light emission under near ultra-violet (UV) excitation. Our results provide fundamental understanding of the Mn defects behavior and the corresponding red-light emission in Mn-doped magnesium fluorogermanate. (paper)