The coupling disturbance between the manipulator and the unmanned aerial vehicle (UAV) deteriorates the control performance of system. To get high performance of the aerial manipulator, a robust fractional order fast terminal sliding mode control (FOFTSMC) strategy based on mutable inertia parameters is proposed in this paper. First, the dynamics of aerial manipulator with consideration of the coupling disturbance is derived by utilizing mutable inertia parameters. Then, based on the dynamic model, a robust FOFTSMC algorithm is designed to make the system fly steadily under coupling disturbance. Furthermore, stability analysis is conducted to prove the convergence of tracking errors. Finally, comparative simulation results are given to show the validity and superiority of the proposed scheme.