Abstract: The aim of this paper is to present a novel time integration algorithm with a high level of balance among applicability and reliability and computational efficiency for the dynamic analysis of structures. A formula for approximating acceleration with a forth-order degree of accuracy has been developed, based on the Taylor expansion approach. In applying the Taylor expansion method, a truncation parameter is defined to consider the contributions of high-order terms upon the accuracy of predicted results. Through an integration of the obtained acceleration and considering the dynamic equilibrium condition at the initial state of a typical time step, a single-step equation for computing displacement and velocity at the end state is correspondingly developed. A revised acceleration can be obtained from the calculated displacement and velocity through the equations of motion at the end state. In this regard, as compared with the multiple-step integration scheme, it is not required for the present method to temporarily record the state variables of previous steps. From the results of stability analysis, the maximum step length to period ratio within which the obtained responses remain bounded has been increased by 40% in comparison to the central difference method. By carrying out a series of numerical analyses for the purpose of demonstration, it is generally observed from the natural and forced vibration investigations for linear systems that the computational amplitude decay and period elongation were less than 5% even if the ratio between the time step length and system inherent period/load period mounts to 0.2. However, to reduce the effects of amplitude decay and period distortion for the time integration of nonlinear systems, the magnitude of the above mentioned ratio should generally be restricted below 0.1.