We report low temperature (80 K) photoluminescence studies of microcrystalline diamond with germanium-vacancy (GeV) centers under hydrostatic pressure up to 6 GPa. Powders of Ge-doped diamond crystals were synthesized from hydrocarbons at high-pressures and high- temperatures. Due to the high quality of the samples, we were able to resolve the distinct quadruplet structure of the zero-phonon line (ZPL) of the GeV center already at 80 K and to trace it up to ∼ 6 GPa. The pressure dependence of ZPL was found to be linear with the pressure coefficient dE/dP = 3.1 meV/GPa, which is nearly 3 times higher than that for the isomorphic SiV− center. The experimentally observed pressure coefficients of GeV−, NV− and NV0 centers are compared with results of ab-initio DFT calculations, using Quantum ESPRESSO software package.