Luo was born in the UK[2] but grew up in Xi'an in a family of artists.[4] After earning bachelor's and master's degrees in theoretical mechanics at Xi'an Jiaotong University, in 1982 and 1985 respectively, she became a lecturer at Xi'an Jiaotong University. There, she studied for a Ph.D. from 1987 until 1990,[4][5] with a visit to the UK through a joint doctoral program with the University of Sheffield. When she earned her Ph.D. at Xi'an Jiaotong University in 1990, she became the first woman to do so.[4]
She moved to the UK in 1992 to become a postdoctoral researcher at the University of Leeds. She worked as a lecturer in engineering at Queen Mary and Westfield College from 1997 to 2000, and in mechanical engineering at the University of Sheffield from 2000 to 2004, before becoming a senior lecturer in mathematics at the University of Glasgow in 2005. She was promoted to professor in 2008,[4][5] the first female professor of applied mathematics at Glasgow.[2]
In 2014 she was named a chair professor at Northwestern Polytechnical University in Xi'an.[2] She has also been a visitor to the International Center for Applied Mechanics at Xi'an Jiaotong University.[1]