Laser-induced magnetization precessional dynamics was investigated in epitaxial films of Mn3Ge, which is a tetragonal Heusler-like nearly compensated ferrimagnet. The ferromagnetic resonance (FMR) mode was observed, the precession frequency for which exceeded 0.5 THz and originated from the large magnetic anisotropy field of approximately 200 kOe for this ferrimagnet. The effective damping constant was approximately 0.03. The corresponding effective Landau-Lifshitz constant is approximately 60 Mrad/s and is comparable with those of the similar Mn-Ga materials. The physical mechanisms for the Gilbert damping and for the laser-induced excitation of the FMR mode were also discussed in terms of the spin-orbit-induced damping and the laser-induced ultrafast modulation of the magnetic anisotropy, respectively.