In this paper, we develop a reliable Linear Parameter-Varying (LPV) model of the pitch channel dynamics of a fin-stabilized projectile. Among the available LPV design approaches, the State Transformation is analyzed, being particularly suitable for a class of systems defined as output nonlinear, and compatible with the projectile dynamics formulation. The State Transformation provides a quasi-LPV representation, which corresponds to an exact transformation of the original nonlinear model, preserving relevant couplings that are usually lost through the classical approximation methods. Some important considerations regarding the limitations of this approach are also discussed and verified in the missile dynamics. The accuracy of the obtained quasi-LPV model is assessed by means of open-loop simulations, comparing the performance to the original nonlinear model at selected flight conditions.