In this paper, a novel finite-time attitude control law is proposed for rigid-flexible coupling satellites in large angle manoeuver. First, the rigid-flexible coupling dynamic model is set up to reflect the coupling effect between the deformation of flexible appendages and the spatial movement of the rigid hub. Then an extended state observer (ESO) is designed to estimate and compensate the total perturbation including high-order flexible coupling terms, external disturbances and uncertain inertia. Following this, a continuous finite-time attitude controller is designed based on non-singular fast terminal sliding mode (NFTSM) and fast power reaching law, which is introduced to smooth the control input and eliminate the chattering. Numerical simulation is designed to verify the finite-time stability, high accuracy, disturbance rejectionand vibration damping of the proposed control scheme and then a ground experimental system is set to further test the controller's practicability.