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This article presents a mathematical model and a controller for a convertible fixed-wing Vertical Take-Off and Landing (VTOL). The mathematical model considers the aerodynamic forces generated by the motors. The developed Passivity-Based Control (PBC) law stabilizes the rotational and translational dynamics of a convertible Unmanned Aerial Vehicle (UAV) in the transition stages of cruise-stationary flight. The control objective is to allow the realization of the two flight regimes of a convertible VTOL along a trajectory. A control assignment technique is also presented that allows the decoupling of the angles of the front motors so that they can have different positions. Finally, numerical simulations are carried out to validate the performance of the presented algorithm. The results indicate that this controller can provide enough maneuverability to track different trajectories with good performance.