The structures, relative stabilities, and electronic properties of size-selective single Hf-encapsulated germanium caged clusters (n = 9-24) have been investigated in detail by density functional method for the first time. The dominant growth behavior of the solid nanocluster Hf@Ge-n is based on a pentagonal prism instead of a hexagonal prism. Analogous to Hf@Si-n, the encapsulated fullerene-like structure of Hf@Ge-n begins to appear at 14, which is consistent with the prediction from the reactivity toward water in a recent experiment (J. Phys. Chem. A 2007, 111, 42). Also, similar to Hf@Si-n in the previous experimental observation (Chem. Phys. Lett. 2003, 371, 490), the binding energy of Hf@Ge-n is gradually increased up to the maximum at 16 and tends to be decreased subsequently, suggesting that stabilization of large germanium cages needs to be realized by doping more Hf atoms. The encapsulated Hf will obviously be moved away from the center of the germanium cage if the cluster size of Hf@Ge-n is larger than 20. According to analysis of the electron density of size-selective Hf@Ge-n, the covalent character in the germanium framework can be affected by the encapsulated position of Hf in the germanium cage. In addition, comparison between typical low-lying size-selective Hf@Ge-n and Hf@Si-n (n = 12, 16 and 20) cages indicates that large-scaled divergence exists in stabilities, growth behaviors, electronic properties, and so forth.