Dust charging in an unmagnetized collisionless dusty plasma with two-temperature electrons was investigated based on the orbital motion limited theory, where the two-temperature electrons and ions are modelled by the Maxwellian distributions. Then by taking into account the effects of two-temperature electron and the associated charging fluctuations, the dispersion peculiarities of dust-acoustic waves are studied based on dust fluid dynamics. The present results show that the effect will introduce a dissipation on the mode, and the dispersion and the dissipation depend on the temperature ratio and number density ratio of hot and cold electrons.