To address the issue of inaccurate modeling during the deformation of hypersonic aircraft, a linear parameter variable (LPV) modeling method is proposed. First, considering its complex characteristics of high supersonic speed and complex motion, a nonlinear rigid-body longitudinal motion model for the hypersonic aircraft is established. Next, based on the least-squares principle, the relationship between aerodynamic coefficients and deformation rates is identified, along with an aerodynamic model that includes deformation rates, leading to a longitudinal aerodynamic model for the hypersonic deformable aircraft. Finally, the nonlinear equations are linearized using the Jacobian linearization method, and a parameter-varying LPV model is fitted, which closely approximates the motion response when compared to the nonlinear model, as validated through simulations. Based on the LPV model, control methods are studied, and simulation experiments demonstrate that the aircraft model under this modeling approach achieves better tracking accuracy with a unified performance optimal controller, thus confirming the effectiveness of this modeling method.