The work is devoted to the investigation of a paramagnetic germanium-vacancy defect in diamond using the density functional theory (DFT) cluster method. The structure and electronic properties of the defect were analyzed. Particular attention was paid to spin-Hamiltonian parameters. The symmetry, g-tensor, hyperfine interaction constants, and zero-field splitting (ZFS) parameter obtained were compared with the previously published experimental data. We found that the neutral germanium split-vacancy defect (S = 1) was consistent with the experimental results. The observed large value of the ZFS parameter D can be explained by the spin-orbit coupling contribution. The computational approach was also examined on the well-studied neutral silicon-vacancy paramagnetic center (S = 1), giving the reasonable agreement with the experimental parameters.