This paper presents a novel unmanned aerial vehicle known as the “Penta-jet”, which uses mini turbojet engines as its power source. The Penta-jet offers superior power compared to small rotorcraft and demonstrates enhanced maneuverability during takeoff and landing in comparison to fixed-wing aircraft. The Penta-jet uses four small thrust turbojet engines to supply steering power and a large thrust turbojet engine to provide the main thrust. To analyze the motion characteristics of the Penta-jet, a mathematical model is proposed, focusing on the dynamic analysis of the aircraft’s power system and rotation vector system. To achieve fixed-point reach and trajectory-tracking tasks, a back-stepping control technology with integral terms is designed for the attitude subsystem (inner loop) and position subsystem (outer loop). Simulation results demonstrate the proposed control method has a shorter adjustment time and smaller overshoot compared with the traditional control method, especially in tracking spiral trajectories.