Hydrogen-rich materials have fascinating physical and chemical properties such as various structures and superconductivity under high-pressure. In this study, structural, electronic, dynamical, and superconducting properties of GeH4(H2)2 are investigated based on the first-principles calculations. We first predict several phase transitions of GeH4(H2)2 under pressure. Below 28 GPa, two degenerated structures with I4?m2 and Pmn21 symmetries are preferred, which can be viewed as the distortion of the experimentally observed fcc structure. Then, the GeH4(H2)2, via a triclinic phase that stabilizes in the pressure range of 28?48 GPa, transforms into a metallic orthorhombic phase in which appears the metallization induced by pressure. Another metallic phase with P21/c symmetry enters the phase diagram at around 220 GPa, which is more stable than the case of a decomposed material, and its stability is also confirmed by including the zero point energy correction. In the high-pressure P21/c phase, the superconductivity is found, and the superconducting transition temperature is predicted to be as high as 76?90 K at 250 GPa. This superconductivity mainly results from the local vibrations of more H2 units, though the vibration of Ge in an H2-formed grid also contributes to the electron?phonon interaction. This study is helpful for understanding the superconducting mechanism on hydrogen-rich compounds.