This paper proposes an Model Predictive Control (MPC) integrated framework to enhance the trajectory tracking accuracy and robustness of quadrotor in dynamic environments. Addressing challenges in precision and disturbance rejection, the framework leverages a manifold-based MPC to directly optimize thrust and moments inputs while compensating for aerodynamic drag and external disturbances. By utilizing differential flatness for reference trajectory, the method formulates the control problem as a Quadratic Programming (QP) problem to compute optimal control increments. Simulations comparing the proposed framework with a baseline MPC-PID controller demonstrate significant improvements in tracking precision and robustness. The results validate that the control framework effectively balances computational efficiency with accurate control, enabling agile trajectory tracking even under external disturbances. This work advances the practical deployment of quadrotor in real world scenarios requiring agile and precise motion control.