Stratospheric airships, serving as broadband telecommunications repeater platforms, face challenges in maintaining attitude stability due to parameter uncertainties, especially at hover mode. This paper presents an adaptive attitude dynamics model for hover mode, followed by the development of an adaptive backstepping control law to compensate for these uncertainties. The stability of the system under the proposed control is then analyzed using the Lyapunov function. The effectiveness of this control algorithm in ensuring stable attitude control is confirmed through simulation experiments, demonstrating its potential in improving the reliability and performance of airships.