Dust is a tiny solid particle that influences the physical properties of galaxies, depending on the size distribution or quantity of dust.Thus, proper treatment of dust evolution is fundamentally important to understand the formation and evolution of galaxies.Asano et al. (2013a, b, 2014) proposed a comprehensive theoretical model (hereafter Asano model) which consistently solves the chemical evolution of dust in galaxies. we developed a new version of the Asano model, implementing the inflow of gas from intergalactic space. We found that even if the gas is significantly consumed to form stars, dust can grow in the interstellar matter infalling from outside of a galaxy. This can supply sufficient amount of dust at a young galaxy age when the stellar mass is quite small.