This paper presents a mathematical model and vertical flight control algorithms for a new tilt-wing unmanned aerial vehicle (UAV). The vehicle is capable of vertical take-off and landing (VTOL). Due to its tilt-wing structure, it can also fly horizontally. The mathematical model of the vehicle is obtained using Newton-Euler formulation. A gravity compensated PID controller is designed for altitude control, and three PID controllers are designed for attitude stabilization of the vehicle. Performances of these controllers are found to be quite satisfactory as demonstrated by indoor and outdoor flight experiments.