Electric field-induced pattern formation of two-dimensional smectic-A filaments have been observed in the binary mixture of octyloxycyanobiphenyl and dodecyl alcohol. As the mixture is cooled below its transition temperature, the smectic-A phase grows into a collection of filaments directly from an isotropic phase. Without the electric-field application, these filaments, which have fixed radius, buckle three-dimensionally as they grow. When the liquid crystal samples are subjected to electric field, the three-dimensional patterns of smectic-A filaments are changed to two-dimensional periodic wavy patterns of the filaments. The two-dimensional pattern is formed on a plane perpendicular to electric field. To understand the electric field-induced two-dimensional pattern formation process, the shape equations for the filaments have been derived by a variation of the sum of Gibbs free energy, curvature elastic energy, surface energy, and dielectric energy. An analytical solution to the shape equations are derived, and shown to be in good agreement with the experimental observation.