Cooperative transportation of cable-suspended load with multi-Unmanned Aerial Vehicles(UAVs) poses challenges in trajectory tracking due to its under-actuated nature. The traditional PID control method encounters difficulties in addressing multi-objective control optimization problems, as well as demonstrating limited tuning capability. To address these issues, this paper proposes a multi-level and distributed cooperative control system based on load leadership. This approach enables precise modeling of subsystems while simplifying control algorithms. Taking into account vehicle acceleration limitations and inter-UAVs safe distance constraints, model predictive control (MPC) is utilized as the formation controller, coupled with an internal feedback controller, to achieve position control of the payload. Simulation experiments comparing this approach with double closed-loop cascade PID control demonstrate superior tracking accuracy, particularly evident in figure-of-eight trajectory tracking scenarios.