The photoionization cross sections of the 4s-main line and the corresponding satellite lines of the Kr atom are studied experimentally and theoretically in the near-threshold region. Our measurements have been made using the photon induced fluorescence spectroscopy technique. Many-electron correlations have been accounted for in the calculations. It was shown that the interference of the direct-ionization channel and the channel of the ionization through the decay of the intermediate doubly-excited states explains the experimentally observed complex resonant structure of the 4s-photoabsorption spectrum of the Kr atom.