To address the high-precision trajectory tracking control problem for aerial robot under compound disturbances, this paper proposes a sliding mode control strategy based on a fixed-time disturbance observer. First, considering the coupled effects of centroid offset after target grasping and turbulent wind fields, a six-degree-of-freedom dynamic model is established using the Newton-Euler formula and design a fixed-time convergent compound disturbance observer for disturbance estimation. Second, for the position control subsystem, a nonsingular fast terminal sliding mode controller based on a novel reaching law is designed, which can effectively avoid the system falling into a singular state while enhancing the system's dynamic response performance. For the attitude control subsystem, a hybrid control strategy integrating integral backstepping is proposed to improve the system robustness against external disturbances. Finally, simulation comparisons are conducted to validate the effectiveness of the proposed approach.