The neutron capture cross sections of the stable krypton isotopes were determined in the energy interval from 4 to 250 keV using a C6D6-detector system in conjunction with the time-of-flight technique. The energy resolution of the measurement was 4% at 20 keV and 6% at 100 keV, and the experimental uncertainties were typically 6 to 10%. The measurements were complemented by statistical model calculations of all krypton isotopes in the mass range 78 < A < 86 to also obtain reliable cross sections for the unstable nuclei 79,81,85Kr. These calculations were based on local systematics for all relevant parameters, and the results were estimated to show uncertainties of 20 to 25%. Maxwellian average cross sections were calculated for kT = 30keV.