When an unmanned aerial vehicle (UAV) navigates reactively over an unknown land, it may encounter terrains that require aggressive maneuver to keep the designed coasting speed while staying on the path. During this execution of the aggressive maneuver, the UAV can experience singularity. In this article, a vertical loop aggressive maneuver performed by a quadrotor UAV is investigated. Due to the physical configuration of the quadrotor, the conventional modeling and tracking control method may not be desirable if certain requirements, such as fast coasting speed and sharp turns, are imposed. In this work, a new modeling and maneuver control method, which is called the controlled loop path following (CLPF) method is developed. As shown in numerical examples, the proposed singularity-free model and control method enables a quadrotor to be operated in aggressive maneuverability with features like automatic flipping and precise trajectory following.