The structural, electronic and magnetic properties of germanene adsorbed with 10 different 3d transition metal (TM) atoms have been investigated by using the spin-polarized DFT calculations. The 3d TM adatoms we considered prefer to bind to the hexagon hollow site of germanene, except Zn which favors to bind to the valley site. A strong covalent bonding character between TM adatom and germanene layer is found in most of TM/germanene adsorption systems. By means of adsorption, the germanene can exhibit various electronic and magnetic properties depending on the adatom species, such as nonmagnetic metal (Cu adsorption), nonmagnetic semiconductor (Ni or Zn adsorption), ferromagnetic metal (Cr or Mn adsorption), ferromagnetic semiconductor (V adsorption), and more particular, ferromagnetic half-metal (Sc, Ti, Fe or Co adsorption) with 100% spin-polarization at the Fermi level. In addition, Cr adatom introduces the largest magnetic moment in germanene, while Sc, Ti, V, Mn, Fe and Co adatoms all generate nearly integer magnetic moments. The effects of the on-site Coulomb interaction as well as the magnetic interaction between TM adatoms on the stability of the half-metallic TM/germanene systems are also considered, and the results show that the half-metallic states for the Sc/germanene and Ti/germanene are all robust. These ferromagnetic TM/germanene systems should have potential applications in the fields of two-dimensional spintronics devices. The analysis of the PDOS indicates the ferromagnetic property of the obtained TM/germanene systems mainly resulted from the spin-split of the TM 3d states.