We investigate the time evolution of dust properties, molecular hydrogen (H2) contents and star formation histories in galaxies by using our original chemodynamical simulations. The simulations include the formation of dust in the stellar winds of supernovae and asymptotic giant branch (AGB) stars, the growth and destruction processes of dust in the interstellar medium (ISM), the formation of polycyclic aromatic hydrocarbon (PAH) dust in carbon-rich AGB stars, the H2 formation on dust grains and the H2 photodissociation due to far-ultraviolet light in a self-consistent manner.We focus mainly on disc galaxies with the total masses ranging from 1010 to 1012M⊙ in this preliminary study. The principal results are as follows. The star formation histories of disc galaxies can be regulated by the time evolution of interstellar dust, mainly because the formation rates of H2 can be controlled by dust properties. The observed correlation between dust-to-gas-ratios (D) and gas-phase oxygen abundances [AO ≡ 12 + log (O/H)] can be reproduced reasonably well in the present models. The discs show negative radial gradients (i.e. larger in inner regions) of H2 fraction (fH2 ), PAH-to-dustmass ratio (fPAH), D and AO, and these gradients evolve with time. The surface mass densities of dust (Σdust) are correlated more strongly with the total surface gas densities (Σgas) than with those of H2 (ΣH2 ). Local gaseous regions with higher D are more likely to have higher fH2 in individual discs and total H2 masses (MH2 ) correlate well with total dust masses (Mdust). More massive disc galaxies are more likely to have higher D, fPAH and fH2 , and smaller dust-to-stellar mass ratios (Rdust = Mdust/Mstar). Early-type E/S0 galaxies formed by major galaxy merging can have lower Rdust than isolated late-type disc galaxies. We also compare between galactic star formation histories in the metallicity-dependent and dust-dependent star formation models and find no major differences. Based on these results, we discuss the roles of dust in chemical and dynamical evolution of galaxies. © 2013 The Author Published by Oxford University Press on behalf of the Royal Astronomical Society.