A nonlinear adaptive trajectory tracking control strategy is proposed for a fully actuated stratospheric airship subject to uncertain mass and inertia parameters. Based on the stratospheric airship trajectory tracking model, a non-certainty equivalence adaptive control approach is adopted to estimate the uncertain parameters since its excellently attractive property of the immersion and invariance manifold condition.The key idea involves a new filter construction for the regressor terms in the airship dynamics that enables the establishment of a stabilizing mechanism within the adaption process for uncertain parameters. It is proved that trajectory tracking errors asymptotically converge to zero within the Lyapunov framework. Numerical simulations are presented to demonstrate the performance of the proposed controller.