Acrylonitrile, an acrylic ester such as ethyl acrylate, n-propyl acrylate, n-butyl acrylate, isopropyl acrylate, n-hexyl acrylate and the like are copolymerized with a cross-linkable monomer, an unsaturated organic acid and a vinyl monomer in a one-step or two-step operation to prepare a water-dispersion varnish for electrodeposition which has excellent dispersion stability and gives a coated film having excellent scrape abrasion resistance and high cut-through temperature.