Abstract: A correction method is presented which can effectively improve the spurious oscillation phenomenon in impact problems. Based on the finite element method, the Lagrange multiplier method is introduced to impose contact constraints, and an unconditionally stable implicit combined time integration algorithm is combined to solve the frictionless dynamic contact problem. By introducing additional Lagrange multipliers, the velocity and acceleration obtained by the combined time integration algorithm are modified to meet the persistency conditions of the contact constraints in the form of velocity and acceleration. Numerical example results show that the correction method can effectively improve the spurious oscillation of velocity, contact force, etc. at the time of initial contact, and improve the solution accuracy of impact problems.