The application scope of unmanned aerial vehicles (UAVs) is increasing along with commensurate advancements in performance. The hybrid quadrotor vertical takeoff and landing (VTOL) UAV has the benefits of both rotary-wing aircraft and fixed-wing aircraft. However, the vehicle requires a robust controller for takeoff, landing, transition, and hovering modes because the aerodynamic parameters differ in those modes. We consider a nonlinear observer-based backstepping controller in the control design and provide stability analysis for handling parameter variations and external disturbances. We carry out simulations in MATLAB Simulink which show that the nonlinear observer contributes more to robustness and overall closed-loop stability, considering external disturbances in takeoff, hovering and landing phases. The backstepping controller is capable of decent trajectory-tracking during the transition from hovering to level flight and vice versa with nominal altitude drop.