Abstract: The Ge-72(n, gamma) cross section was measured for neutron energies up to 300 keV at the neutron time-of-flight facility n_TOF (CERN), Geneva, for the first time covering energies relevant to heavy-element synthesis in stars. The measurement was performed at the high-resolution beamline EAR-1, using an isotopically enriched (GeO2)-Ge-72 sample. The prompt capture gamma rays were detected with four liquid scintillation detectors, optimized for low neutron sensitivity. We determined resonance capture kernels up to a neutron energy of 43 keV, and averaged cross sections from 43 to 300 keV. Maxwellian-averaged cross section values were calculated from kT = 5 to 100 keV, with uncertainties between 3.2% and 7.1%. The new results significantly reduce uncertainties of abundances produced in the slow neutron capture process in massive stars.