In a tethered satellite system on elliptical orbits, its in-plane angle can exhibit chaotic behavior. Due to the inherent unpredictability of chaos, conventional control methods often fail to stabilize the system. As the orbital eccentricity increases, the chaotic behavior becomes more pronounced, and the system may even exhibit global chaos. To broaden the application scenarios of the tethered satellite, it is necessary to design corresponding chaos suppression algorithms to make it stable. In order to guide chaotic motion to regular motion, two control methods are proposed: one based on tether speed and the other based on tether tension. In the speed mode, Ott-Grebogi-Yorke (OGY) method and Delayed Feedback Control (DFC) method are introduced to gradually guide the system towards regular motion by controlling the length of the tether. In tension mode, a tracking differentiator and a tracking controller are designed to track the output in speed mode. By controlling the tether's reeling in and out, the system states can converge to fixed values on the Poincaré section, thereby escaping chaos. Finally, the effectiveness of the proposed control scheme is verified by numerical simulation.