In the present study, a compressible anisotropic hyperelastic strain energy density function (SEDF) is developed to capture the in-plane nonlinear elastic responses of a commercial Fiberglass/Phenolic hexagonal cell honeycomb core under large deformations. A 3D nonlinear finite element model (FEM) with large displacements of the representative unit cell of the periodic core microstructure is employed to generate homogenized stress-strain curves of the core to assemble the hyperelastic SEDF using curve fitting methods. The hyperelastic constitutive model is evaluated using a single element model in the finite element program on which simple states of loading are imposed. Good agreement is observed between the model predictions and test results. The proposed model can be used as an effective constitutive model of the homogenized core to study the behavior of the core under complex loading and boundary conditions such as simulations of honeycomb core forming processes wherein the honeycomb core cells experiences large in-plane deformations owing to the flexural deformation.