This paper considers a quadrotor transportation system with a four-cable-suspended payload. The relative position be tween quadrotor and payload is introduced and used to derive the tension of cables and describe the transportation system. A cost function inspired by payload and time is built to equipoise rapid UAV positioning and payload swing elimination. Then， the pseudo spectral method is applied to transform the optimal control problem into a nonlinear programming problem and solve the optimal tra jectory. A quadrotor transportation system’s trajectory tracking is facilitated by a PID controller. The optimal trajectory is validated through the presentation of both simulation and experimental results at last.