Xu received his bachelor's degree from the Xiangtan University in 1982, his master's degree from the Peking University in 1984, and his doctoral degree from the Cornell University in 1989. He joined the Pennsylvania State University (Penn State) in 1989 as assistant professor of mathematics, was promoted to associate professor in 1991, and to professor in 1995. He was named a Distinguished Professor of Mathematics in 2007, the Francis R. and Helen M. Pentz Professor of Science in 2010, and the Verne M. Willaman Professor of Mathematics in 2015.

Xu serves on the editorial boards of many major journals in computational mathematics and co-edits many conference proceedings and research monographs. He also serves on various college and departmental committees and organizes numerous colloquiums and seminars. He has organized or served as a scientific committee member for more than 65 international conferences, workshops, and summer schools.