According to the charging equation and charge conservation, the charging frequency (electric relaxation rate) is deduced and the formulation of charging electric current of the weakly ionized dust plasma is given according to the double Maxwellian distribution. It is shown that the directional speed have an influence on charging frequency; the charging frequency will decrease with the increase of directional speed; the charging frequency expression are the same as that in the literature when the directional speed is much smaller than the electron thermal velocity.