Abstract: An implicit high-order accurate time integration method is presented based on the weak form Galerkin method.In each time element,approximate solution is constructed by the Lagrangian interpolation functions.Three formulations,which are two-,four-,six-order of accuracy,are obtained by using linear,quadratic and cubic Lagrangian interpolation functions.When solving the equations,unknown displacements in the time elements are eliminated first to make the method more effective.Stability analysis shows that the formulations are conditionally stable.By using reduced integration,three unconditionally stable formulations are obtained.Numerical examples are included to illustrate the behavior of these algorithms.The results show that their precision and efficiency are remarkably higher than those of the Newmark method.