In this talk,we will introduce the recent development on constructing the energy- preserving methods based on Hamiltonian Boundary Value Methods (HBVMs) for a given Hamil- tonian ODEs.For the general Hamiltonian systems,there is no Runge-Kutta method which can preserve the energy even for the system with polynomial vector field.We have proved that the only exception is the Averaged Vector Field (AVF) method which can be reformulated as a Runge-Kutta method for the polynomial Hamiltonian systems.