In analyses of the scanning vibrating electrode technique (SVET), the conductivity of the electrolyte solution near the specimen is usually assumed to be uniform over space and constant over time when calculating the current density. These assumptions may be inadequate in practice, and non-uniformity due to electrolysis should not be ignored. To overcome these limitations, ion transport is considered in a dilute solution. To describe the ion concentration and electric field change close to the specimen surface, a model is used that employs the Nernst-Planck equation and the electro-neutral condition. A finite difference method is used to solve the resulting time-dependent axisymmetric problem. The computational results show good agreement with the experimental data obtained by SVET. It is also found that the electric potential gradient reduces to one-tenth of the initial value and of the result predicted by the conventional model with uniform conductivity.