The design of a Model Predictive Controller (MPC) for attitude maneuvers of an Unmanned Vertical Take Off and Landing (VTOL) Tilt-Rotor vehicle, flying in its helicopter mode is the subject of this article. Tilt-Rotor air vehicles combine the flight envelopes of: a)fixed wing aircrafts, and b) rotorcrafts, leading to systems with advanced flight characteristics. However, the highly nonlinear and underactuated dynamics of these systems, necessitate the design of advanced control schemes to achieve a satisfactory control performance. In the proposed control design approach, the Tilt-Rotor's nonlinear dynamics are linearized in various operating points, resulting in a set of multiple piecewise affine models that describe its helicopter's flying mode. The corresponding novel MP-controller is designed for set-point maneuvers taking into account the arbitrary switchings between the linear models as well as the constraints on the actuators, while extended simulation studies indicate the high overall efficiency of the proposed MPC scheme.