Liu was born in Liuyang, Hunan in 1943. He received his Bachelor degree from National Taiwan University in 1965 and his Ph.D degree from the University of Toronto in 1971.
He is a book writer and has published a fiction novel of ancient Chinese rovers practicing martial arts.
Liu started to receive public attention when he was the President of National Tsing-hua University in Hsinchu before 1993. At that time, he and his school had just successfully hosted the annual united college-entrance examination for Bachelor degree in Taiwan.
Then, Liu was given the post of Minister of Transportation, from 1993 to 1996. He was Vice-Premier from 1997 to 2000. He became the President of Soochow University in 2004.
Liu was selected by current President Ma Ying-jeou to become the Premier of the Republic of China in April 2008. His term as Premier took effect with Ma's incoming administration on May 20, 2008.