Here we report the voltammetric behavior of cone-shaped silica nanopores in quartz nanopipettes in aqueous solutions as a function of the scan rate, v. Current rectification behavior for silica nanopores with diameters in the range 4-25 nm was studied. The rectification behavior was found to be strongly dependent on the scan rate. At low scan rates (e.g., v < 1 V/s), the rectification ratio was found to be at its maximum and relatively independent of v. At high scan rates (e.g., v> 200 V/s), a nearly linear current voltage response was obtained. In addition, the initial voltage was shown to play a critical role in the current voltage response of cone-shaped nanopores at high scan rates. We explain this v-dependent current-voltage response by ionic redistribution in the vicinity of the nanopore mouth.