Hybrid UAV has combined characteristics of fixed-wing UAV and multi-rotor UAVs. Fixed-wing UAV has higher flight endurance, while the multi-rotor UAV requires no runways and can also perform vertical take-off and landing. Hybrid morphing wing UAV has ability to perform mission both as quadcopter and fixed-wing aircraft combined in efficient manner. This paper discusses the flight capability of a hybrid UAV that can transition between fixed-wing and quadcopter mode of flight. Dynamic equations of the hybrid UAVs are presented. The paper proposes a single non-linear controller with ability to handle the two different flight modes. The proposed controller uses a novel backstepping method and quaternion formulation, as transition between Euler angles provides problems like singularities. Although, backstepping has been used in various control design,it is unique to use backstepping that handles the complex vehicle transition phase along with use of quaternions. The performance of the proposed scheme is demonstrated via numerical simulations.