A Quad-rotor, which is an airplane with four rotors, is considered a complex and challenging control problem. Analysis and design of its control systems is usually started by careful consideration of its mathematical models description. This paper presents a detailed mathematical model for a Vertical Takeoff and Landing (VTOL) type Unmanned Aerial Vehicle (UAV) known as the quad rotor. The presented paper focus on the nonlinear modeling of an experimental type quad-rotor. The first objective of this paper aims to develop a nonlinear dynamical model based on Newton-Euler approach. Then, a linear model is obtained around an optimized hovering point. The state space, transfer function matrix and matrix fraction description models are derived. Finally, a linear controller is designed to achieve a stable compensated system around a hovering point. The methodology applied in this paper takes the ST-450 experimental quad-rotor as a case study.