Tethered quadrotors, unmanned aerial quadrotors connected to a fixed point via tether cables, have been widely applied in numerous aerial tasks. However, their structural parameters and external disturbances give rise to dynamic stability issues, resulting in uncontrolled autonomous flight, shaking, and vibrating. Thus, this article investigates the quantitative stability of a tethered quadrotor using the Lyapunov exponent approach. First, a mathematical model of the tethered quadrotor is developed, and its dynamic stability is quantified to verify the rationality of the designed physical prototype and enhance the aerial system’s stability. Both simulation and experimental results show that the dynamic stability during the landing phase is better than that during takeoff. Finally, optimizing the structural parameters enhances the dynamic stability, which is sensitive to cable length, wind gusts, and yaw angle.