Four Cosmological distances were determined in the light of the closed cosmic model which was presented in a previous study. Each of these distances was obtained in terms of the redshift of an extragalactic object. It is found that the luminosity distance of the extragalactic object in the closed cosmic model, the observed model and model are approximately the same up to z = 0.1535. However, the luminosity distance in the close cosmic model approximately agrees with its value in the observed model up to z = 0.6442. Estimations of the horizon distance of the universe, the total mass and the mass of matter within the horizon distance, the equivalent numbers of the Milky Way-like galaxies and the Coma-like clusters of galaxies to the mass of matter were computed in the closed cosmic model at the present time.