Numerical integration methods of traditional pseudo-dynamic test are mainly divided into two kinds of explicit and implicit algorithms. Previous studies have shown that explicit algorithm is more suitable for pseudo-dynamic testing than the implicit method. However, explicit algorithm itself has many inherent defects. Also, it is necessary to make improvements on the algorithm since the requirements of modern teaching and research on the precision of pseudo dynamic tests results are more and more higher. Details of the progress and current status of the research by domestic and foreign scholars on explicit algorithm improvements are demonstrated here. And through discussing and summarizing several major aspects of the improvements of explicit algorithm, several issues which need to be resolved are pointed out, and so the reasonable future research direction and goals are also made.