Abstract: Model order reduction (MOR) approach generates lower dimensional approximations to the original system while preserving model's essential information and computational accuracy. For nonlinear and parameterized structural problems, where the stiffness matrix is configuration dependent, an iterative solution procedure is inevitable and a revisit to all the elements is essential for updating the stiffness matrix. Considering the difference between CAD and finite element models, a preprocessing step is necessary for each parameterized geometry, which is time consuming for complex geometries. Isogeometric analysis (IGA) utilizes non-uniform rational B-spline (NURBS) basis for both the geometry description and physical filed interpolation, thusly eliminates the time-consuming preprocessing step between CAD and finite element models. IGA is a perfect candidate for the analysis and geometry parameterization of thin-walled structures due to its geometrically exact and high order continuous properties. The nonlinear dynamics of the parameterized planar curved beams are studied based on the isogeometric analysis and their model order reductions are investigated based on the proper orthogonal decomposition and discrete empirical interpolation method (POD-DEIM). Numerical results show that IGA-based POD-DEIM method significantly improves the computational efficiency of the nonlinear dynamic analysis of planar curved beams. Additionally, the proposed method also applies to different external loadings and time step sizes, which demonstrate the adaptivity of the method.