Structural and electronic properties of halogen (F, Cl, Br, I, and At)-functionalized armchair germanene nanoribbons (AGeNR) are investigated using the density functional theory (DFT) method. The first-principles quantities are fully developed to determine the studying properties, including the functionalized energies, optimal structural parameters, atom- and orbital-decomposed electronic band structures and density of states, charge density, and charge difference. The halogen-functionalized structures achieve good stability that is determined by the calculated functionalized energies. The pristine AGeNR presents a direct bandgap located at the band-edge states of 0.23 (0.36) eV that opens at 0.76 (1.38) eV under the F-functionalization as calculated by PBE (HSE06) functionals, respectively. The opened bandgaps of 0.73 eV and 0.51 eV are found in the Cl-AGeNR and Br-AGeNR. In contrast, the bandgap is shrunk/destroyed in the I-AGeNR/At-AGeNR, respectively. Besides, a case study of F-functionalized zigzag germanene nanoribbons (F-ZGeNR) is also investigated to compare with the AGeNR case. As a result, the opened bandgap is much larger in the F-AGeNR case than that in the F-ZGeNR case. This indicates that the electronic properties are better enhanced in the AGeNR than that in the ZGeNR. The bandgap-diversified mechanism is due to the termination of free-standing π bonds and complex orbital hybridization in halogen-Ge bonds. Under halogen functionalizations, electrons are transferred from Ge atoms to halogen adatoms that create free holes in the functionalized systems that can be regarded as p-type semiconductors/semimetals. The diverse structural and electronic properties of halogen-functionalized GeNR will be very potential 1D materials for various electronic applications.