This paper deals with the edge effect in thin insulating films, focusing on their dependence on film thickness. The finding is that the electric field is lowered at the edge as the film thickness is reduced, which, in turn, is closely related to dielectric breakdown voltage. In order to analyze this phenomenon, a simple capacitor model is introduced with which dependence of dielectric breakdown voltage around the electrode edge on the film thickness is explained. Due to analytical difficulty to get the expression of electrical field strength at the edge, an equivalent circuit approach is used to find the voltage expression first and then the electric field expression using it. The relation gets to an agreement with the experimental findings shown in the paper. This outcome may be extended to solve similar problems in multi-layer insulating films.