We explore the radiation hydrodynamical evolution of a galactic nuclear gas disk exposed to intense radiation from circumnuclear starbursts. The evolution is characterized by two stages. First, the disk is radially contracted by the radiation force. Subsequently, the surface stratum of the disk avalanches onto the center due to the removal of angular momenta by radiation drag. The mass accretion via a radiatively-driven avalanche was analyzed quantitatively while assuming a torus shape of the circumnuclear starburst regions. As a result, it was found that the mass-accretion rate is sensitively dependent upon the extension of the starburst regions. For an optically thick disk, the mass-accretion rate is roughly in proportion to the ratio of the thickness to the curvature radius of the torus. The rate is also dependent upon the rotation law of the disk. We investigated the evolution of the disk surface density resulting from radiatively-driven mass accretion. It was found that for a more intensive starburst the central concentration of surface density becomes more conspicuous. The present results seem to be significant when considering the evolution of starburst nuclei, for instance, in luminous IRAS galaxies.