A novel distributed-vector-propulsion UAV (DVPUAV) is introduced in this paper, which has the capability of Vertical takeoff and landing (VTOL), and can realize relatively high-speed cruise. As the core of the DVPUAV, the propulsion wing designed under the guidance of the integration idea is not only a lifting body but also a propulsion device and a control mechanism. However, this kind of aircraft has a series of difficult problems with complex aero-propulsion coupling, flight modes switching, and so many inputs and control coupling. In order to describe this coupling effect to improve the accuracy of dynamics, an aero-propulsion coupling model is developed, considering both computation reliability and real-time. Afterward, a unique control framework is designed for the DVPUAV. By optimizing control logic, this control framework realizes the decoupling of longitudinal and lateral directional control and even the decoupling of roll and yaw control. Next, based on the Iterative linear quadratic regulator (ILQR), a new Model Predictive Control (MPC) controller with the ability to solve complex nonlinear problems is proposed which achieves the unification of the controller for the full flight envelope. Finally, the good performance of the control framework and controller is verified in the whole process of the flight simulation from take-off to landing.