This paper considers a hybrid vertical take-off and landing (VTOL) unmanned aerial vehicle (UAV). By tilting its propellers, the aircraft can transition from rotary-wing (RW) multirotor mode to fixed-wing (FW) mode and vice versa. A novel architecture of a neural network-based controller (NNC) is presented. An “imitative learning” approach is employed to train the NNC to mimic the response of an expert but computationally expensive model predictive controller (MPC). The resulting NNC approximates the MPC’s solution while significantly decreasing the computational cost. The NNC is trained on the longitudinal axis. Successful simulations and real flight tests prove that the NNC is suitable for the longitudinal axis control of a complex nonlinear system such as the tilt-rotor VTOL UAV through a sequence of transitions between the RW mode to the FW mode, and vice versa, in a forward flight.