The complex permittivity of weakly ionized dusty plasma is presented as a fractional polynomial in j. A frequency-domain constitutive relation of weakly ionized dusty plasma is given by shift operator finite-difference time-domain (SO-FDTD) method in time domain. Also the recurrence relation on the electromagnetic properties of weakly ionized dusty plasma is deduced by the SO-FDTD. The reflection and transmission coefficients of the weakly ionized dusty plasma layer are calculated, and the influences which is caused by the change of the dust particle concentration and radius on reflection and transmission coefficients are also analyzed by the SO-FDTD method. The result shows that the reflection coefficient in the presence of dust particles is smaller than in the absence of dust particles, while the transmission coefficient in the former case is larger than in the latter case. Besides, it is found that the reflection coefficient decreases as the concentration or radius of dust particle increases.