An impedance control strategy based on non-singular fast terminal sliding modes is proposed to solve the problem of contact control during cooperative transportation of double cable-driven aerial manipulators. Firstly, considering the flexibility effect of the cabledrive mechanism, the dynamics model of the dual-machine collaboration system taking into account the flexibility of the joints is established, and the impedance equation in the task space is derived. Then, a cooperative impedance control strategy is designed to accelerate the system state volume and convergence speed with the use of non-singular fast terminal sliding mode surfaces, and to weaken the output torque jitter effect using power functions. At the same time, the stability of the controller is analysed in the Lyapunov framework. Finally, the effectiveness of the proposed control strategy is verified by controller comparative performance simulation and cooperative transportation simulation. The results show that the proposed controller has fast response speed, high control accuracy and excellent stability, and can effectively reduce the system chattering.