This paper addresses the attitude tracking control problem with uncertain inertia parameters and unmodeled external disturbances. The proposed control method utilizes the fast adaptive control scheme based on the non-certainty equivalence principle and the sliding-mode control technique. The former is dedicated for the compensation of the uncertain inertia-parameter effects and the latter for the disturbance rejection. Therefore, the proposed controller inherits the advantages from both methods represented by the guaranteed transient performance under unmodeled disturbances and the faster asymptotic stability compared to the one based on the certainty-equivalence principle. In order to demonstrate the efficiency of the proposed controller, numerical simulations are performed after the technical discussions on the stability of the controller.