The finite element methods of ordinary differential equations are in the 5-order quantity approximately symplectic conservation for continuous quadratic element of nonlinear Hamiltonian systems, and maintain energy conservation.In the numerical experiments of Hamiltonian chaos's, combining section and sensitiveness to initial value of the Chaos movement, applying the quadratic element methods and comparing with symplectic difference methods, obtains the numerical test results consistent with the theoretical. Provides a better method for studying Hamiltonian chaos .