Based on the density functional theory and first-principal calculations, the physical properties of the Zr3GeO8 crystal for the ground state were calculated. In all calculations, the Density functional theory based ABINIT package program was used. Investigations were made under the local density approximation. The geometric optimization of the Zr3GeO8 crystal, the state density of the valence electrons, the electronic band structure to understand the conductivity character of the crystal, and the linear optical properties to see the response of the material to the electromagnetic wave were calculated. In addition, dynamic-thermodynamic properties were calculated for the Zr3GeO8 crystal. According to the calculated structural optimization and electronic band structure, the band gap of the Zr3GeO8 crystal is 4.4663 eV and it has been obtained that it has an indirect band gap. For the Zr3GeO8 crystal, some constants such as energy loss functions, reflectivity, and absorption coefficient are calculated depending on the ground state linear optical properties and linear optical properties. The phonon distribution, state density and contribution of each atom to the density of state the Zr3GeO8 crystal were calculated. Finally, free energy, internal energy, entropy, and heat capacity were calculated for the Zr3GeO8 crystal.