Molecular dynamics simulations were carried out to explore the capillary wave propagation induced by the competition between one upper precursor film (PF) on the graphene and one lower PF on the substrate in electro-elasto-capillarity (EEC). During the wave propagation, the graphene was gradually delaminated from the substrate by the lower PF. The physics of the capillary wave was explored by the molecular kinetic theory. Besides, the dispersion relation of the wave was obtained theoretically. The theory showed that the wave was controlled by the driving work difference of the two PFs. Simulating the EEC process under different electric field intensities (E), the wave velocity was found insensitive to E. We hope this research could expand our knowledge on the wetting, electrowetting and EEC. As a potential application, the electrowetting of the PF between the graphene and the substrate is a promising candidate for delaminating graphene from substrate.