Abstract: A super convergent explicit second-order precise integration method is presented, which establishes the iterative algorithm for dynamic time history analysis base on the second-order Taylor expansion. The Gauss integral is used to deal with the integration of load term in each iteration step, and the super-convergence factor \alpha and \beta is introduced to improve the convergence and computational stability of the algorithm. The inverse and multiplication of the global stiffness matrix is avoided, so that it is not necessary to assemble the global stiffness matrix and it is a new explicit method for dynamic analysis. This method can be unconditionally stable and greatly improve the convergence step after introducing super-convergence factor. The numerical results show that super-convergence explicit second-order precise integration method has high computational efficiency and algorithm stability compared to traditional explicit precise integration; its accuracy and stability can be consistent with the common integration algorithms under the appropriate analysis time step, with better accuracy stability with the increase of analysis time step.