Abstract: Nearly all adaptive step-size methods with maximum norm in solving motion equations via finite element method require the load term to be continuously differentiable. However, for seismic response which is usually recorded in terms of discrete data, it is difficult for these methods to be directly used due to the possibility that an element may straddle two or more time intervals. This paper proposes an interval-wise adaptive step-size algorithm that adjusts the step-size by bisection method, which can effectively avoid the improper overlapping problem. Some numerical examples are given to show the effectiveness and reliability of the proposed method.