The parametric aeroelastic modeling of a morphing aircraft is a hot topic in the research field of morphing aircraft design. However, the traditional non-parametric aeroelastic dynamic modeling methods have some problems, such as low modeling efficiency and complex aeroelastic analysis for for aeroelastic research of morphing aircraft with structural parametric characteristics. In this paper, a parametric aeroelastic modeling method of folding wing based on the tangent space interpolation is proposed. Firstly, based on the structural finite element models of a folding wing at several folding angles, a parametric structural dynamic model of the folding wing is established by tangent space interpolation. Then, the parametric unsteady aerodynamics is computed by the Doublet Lattice method. At last, the parametric aeroelastic model of the folding wing is obtained by coupling the structural dynamics and unsteady aerodynamics. To verify the accuracy of the parameterized model in the aeroelastic calculation, a small aspect ratio folding wing is taken as the research object. The dynamic characteristics including the natural frequencies, mode shapes, and flutter boundaries at different folding angles are efficiently calculated. In addition, the numerical results computed via the present parametric method are compared with the direct non-parametric method. The demonstration shows that the results from the parametric aeroelastic model is consistent with the direct method for the aeroelastic problems and has the advantage of higher calculation efficiency.