Promising results on LPV design have been recently proposed, concerning the modeling and control of missiles, rockets, and aircraft. However, very few investigations have been focused on the development of guided projectile applications. This paper presents a pure linear parameter varying (LPV) modeling and control design approach intended to improve the range capability of a new class of Long Range Guided Projectiles (LRGP). The investigated concept consists of an asymmetric 155 mm fin-stabilized projectile equipped with a reduced amount of control actuators and characterized by a predominant unstable behavior across the analyzed flight envelope. The main advantages of the LPV design in terms of guaranteed robustness and stability are compared to standard gain-scheduling-based linear time-invariant (LTI) control strategies. A nonlinear simulation scenario is performed in order to assess the reliability of a pure LPV autopilot design, based on the polytopic formulation, across the entire flight envelope, over a local modal control design related to a specific set of flight conditions.