Study of terrestrial impact craters is important not only in the field of the solar system formation and evolution but also of the Galactic astronomy. The terrestrial impact cratering record recently has been examined, providing short- and intermediate-term periodicities, such as, ${sim}26$ Myrs, ${sim}37$ Myrs. The existence of such a periodicity has an implication in the Galactic dynamics, since the terrestrial impact cratering is usually interpreted as a result of the environmental variation during solar orbiting in the Galactic plane. The aim of this paper is to search for a long-term periodicity with a novel method since no attempt has been made so far in searching a long-term periodicity in this research field in spite of its great importance. We apply the cepstrum analysis method to the terrestrial impact cratering record for the first time. As a result of the analysis we have found noticeable peaks in the Fourier power spectrum appear ing at periods of ${sim}300$ Myrs and ${sim}100$ Myrs, which seem in a simple resonance with the revolution period of the Sun around the Galactic center. Finally we briefly discuss its implications and suggest theoretical study be pursued to explain such a long-term periodicity.