This paper is concerned with the direct integration method and an adaptive scheme is dynamic analysis of structures which can reduce the discretization errors in time. A new direct integration method using the Galerkin's weighted residual method and an adaptive algorithm using a hierarchical refinement in time with the fixed step size have been developed. An effective error indicator is derived for a hierarchical refinement. Using the error indicator, the refinement level of the hierarchical function is determined so that the local error of each time step is within a prescribed tolerance range.