The Green-Naghdi model is a type of shallow water wave equations, and its numerical solutions attract much attention recently. We develop a scheme coupling a high-order well-balanced positivity-preserving central discontinuous Galerkin method and finite element methods to simulate the Green-Naghdi equations with both at and non-at bottoms. The numerical scheme is based on a reduction of the original Green-Naghdi model to a system of hyperbolic equations together with a stationary elliptic equation. Numerical results will be presented to validate the numerical model and illustrate accuracy of the numerical schemes. This is a joint work with Mr. Maojun Li (RPI/Chongqing U), Prof. Fengyan Li (RPI) and Prof. Philippe Guyenne (U of Delaware).