Calculations of the static dielectric response epsilon (infinity) of some simple oxide and mixed transition-metal oxide insulators using the weighted density approximation are reported, including in particular the perovskites KNbO3, KTaO3, and BaTiO3. The results show that even though the weighted density approximation makes only small changes to the local density band gaps, the values of epsilon (infinity) are consistently lowered, improving agreement with experiment.