The capture cross section of 238U was measured using the activation technique and 235U(n, f) and 197Au(n, γ) as reference cross sections. Capture events were measured by detection of two prominent gamma-ray transitions in the decay of the 239U daughter nuclide, 239Np, employing a high-resolution Ge(Li) detector. The system was calibrated with the absolutely calibrated alpha-particle emitter, 243Am, which decays to 239Np. Cross-section measurements were carried out at thermal neutron energy and in the neutron energy range from 30 keV to 3 MeV. Emphasis in the higher keV range was on absolute values between 0.14 keV and 1 MeV where the 238U(n, γ) cross section and its ratio to 235U(n, f) are not very sensitive to energy scale uncertainties, and the 238U(n, f) cross section is small. Background from fission products was found to restrict the accuracy of the measured data at energies 1.5 MeV.