Abstract: An explicit series solution of the structural dynamic equation is put forward by introducing Taylor series expansion. The algorithm is based on the coupled precise time integration method and basic assumptions of constant average acceleration method in Newmark family. And the method is used to analyze the structural seismic response. With the explicit property, the method requires no computation of the coupled equation and can effectively reduce memory occupancy and computer cost when the quality matrix is diagonal. The stable conditions of the proposed method are obviously to be satisfied and its accuracy can be controlled by choosing the number of Taylor series. The example shows the efficiency of the method on earthquake action.