A thin polymer film subjected to an electrostatic field may lose stability at the polymer-air interface, leading to uniform self-organized pillars emerging out of the film surface. This paper presents a three dimensional dynamic model to account for the behavior. The coupled diffusion, viscous flow, and dielectric effect are incorporated into a phase field framework. Numerical simulations reveal rich dynamics of the pattern formation process and the substrate effect. The pillar size is insensitive to the film thickness, but the distance between pillars and the growth rate are significantly affected. The study suggests an approach to control structural formation in thin films with a designed electric field.