We present the coarsening dynamics of a liquid-ordered (Lo) domain in a supported lipid membrane under an electric field. In a relatively small nanosmooth region surrounded by geometrical walls of nanocorrugated regions, full coarsening of the Lo domain was produced while in a large nanosmooth region, an intermediate, less-ordered Lo domain was developed so that the diffusion of charged phospholipids in the liquid-disordered (Ld) domain was allowed across the geometrical walls in the presence of an electric field. No appreciable diffusion of the charged lipids into a fully coarsened Lo domain by the electric field implies that the structural ordering of the membrane components plays a significant role on the formation of lipid rafts for biological processes.