A new way to construct high order symplectic algorithms is proposed based on weighted residual method. Firstly

in the time subdomain

the corresponding integral equation of Galerkin method for Hamilton dual equation based on the idea of weighted residual method is proposed

then the generalized displacement and momentum are approximated by the same Lagrange interpolation within the time subdomain

which are substituted into the corresponding integral equation. By numerical integration

the original initial value problem of dynamics is expressed as algebraic equations with displacement and momentum at the interpolation points as unknown variables. For nonlinear dynamic systems

a simple scheme of choosing initial values

which can significantly improve the computational efficiency for NewtonRaphson method

is presented. Finally

the symplecticity and performance of the proposed algorithms are discussed in detail. Compared with the same order symplectic RungeKutta methods

the accuracy of the two methods are almost the same

but the proposed algorithms are much simpler and less computational expense. The numerical results illustrate that the proposed algorithms show good performance in accuracy and efficiency.