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This paper analyzes the stability of in-plane/out-of-plane motion of electrodynamic tether systems in elliptic orbits. The chaotic librational motion of a tether system in elliptic orbit has been studied and controlled by delayed feedback control up to date. Delayed feedback control, however, cannot stabilize the librational out-of-plane motion of a electrodynamic tether system in elliptic orbit with high eccentricity, to an periodic motion, because the system has the odd number of the real eigenvalues of the monodromy matrix greater than one. To overcome this problem, in this paper, a new simple delayed feedback control, named "switching delayed feedback control (SDFC)" is proposed. The effectiveness of the proposed method to stabilize the librational in-plane/out-of-plane periodic motion of an electrodynamic tether system in elliptic orbits with high eccentricity is demonstrated through numerical simulations.