Nonplanar lateral oscillation of a wire electrode, called self-excited oscillation, occurs when high electric voltage is applied between the wire and infinite plate electrodes with corona discharge. The purpose of this paper is to suppress wire oscillation using the nonlinear coupling effect, for a single-degree-of-freedom damped spring-mass system attached to the end of the wire electrode in the axial direction. It is clarified from the theoretical analysis that nonplanar oscillation of the wire decays through the effect of damping force on the supplementary system in the state of internal resonance. Furthermore, an experiment is conducted to confirm the relaxation of the wire oscillation. The experimental result is in good qualitative agreement with the theoretical one.