Electroformation of cell-sized lipid membrane vesicles (giant vesicles, GVs) from egg yolk phosphatidylcholine under applied electric voltage was examined on a substrate of a polymer mesh placed between two planar indium tin oxide coated glass electrodes. Under appropriate conditions, GVs were formed in good yield on meshes of various polymer materials, namely, hydrophobic poly(propylene), poly(ethylene terephthalate), a carbon fiber/nylon composite, and relatively hydrophilic nylon. Arranging threads in a mesh structure with appropriate openings improved GV formation compared to simply increasing the number of threads. For optimal electroformation of GVs, the size and shape of a mesh opening were crucial. With a too large opening, GV formation deteriorated. When the sides of an opening were partially missing, GV formation did not occur efficiently. With an adequate opening, a deposited lipid solution could fill the opening, and a relatively uniform lipid deposit formed on the surface of threads after evaporation of the solvent. This could supply a sufficient amount of lipids to the opening and also prevent a lipid deposit from becoming too thick for electroformation. As a result, good GV formation was often observed in openings filled with swelled lipid.