Duncan was born in 1933 in rural Shelby County, Texas. His Father was a farmer. His mother died of tuberculosis when he was seven and his brother died of blood poisoning in the same year. He lived with his grandmother until he graduated from Shelbyville High School. He joined his Father as a pipeliner and roughneck in the oil and gas fields. Soon after his Father also died of leukemia. Duncan served in the U.S. Army during the Korean War and when he returned in 1955, using the G.I. Bill, he studied Business, Finance and accounting at Massey Business College in Houston while also working at the U.S. Post Office.

In 1957, he went to work for Wanda Petroleum, a midstream pipeline company In 1968, he left Wanda, and with $10,000 and two propane delivery trucks, helped found Enterprise Products Co. In 1998, he took Enterprise Products Partners LP public. In 2010, Enterprise owned over 48,700 miles of onshore and offshore pipelines and nearly 220 million barrel equivalents of natural gas and natural gas liquids of storage capacity. He also headed mid-stream Energy firms Duncan Energy Partners LP (NYSE: DEP) and Enterprise GP Holdings LP (NYSE: EPE). In 2007, he received the Petrochemical Heritage Award in recognition of his work.

Duncan was married to Jan Ellis. He is survived by four children, each of whom is now a billionaire: Randa Duncan Williams (born 1962), Milane Duncan Frantz (born 1970), Dannine Duncan Avara (born 1974), and Scott Duncan (born 1983).

Duncan owned the Double D Ranch, a 5,000-acre (20 km) hunting property in Texas. Duncan was a Safari Club International member who has been given numerous awards for his hunting trophies. In 2006, he received the SCI World Conservation Hunting Award, which requires a hunter to have hunted on six continents, and have received SCI's 13 "Grand Slam" awards, 22 "Inner Circle" awards, the Fourth Pinnacle of Achievement Award and the Crowning Achievement Award. Duncan has 407 entries in SCI's trophy record book, including records for killing lions, elephants, rhinoceroses, a polar bear, and other animals.

On July 18, 2007, Duncan voluntarily appeared before a grand jury in Houston. He answered questions regarding a hunt in Russia in 2002 in which he shot and killed a moose and a wild sheep from a helicopter, which is illegal under Russian law. He admitted to his actions, but said that he did not know that his actions were illegal. His attorney said on September 12, 2007 that a grand jury had declined to bring charges against Duncan and other Hunters who had been on the trip.

According to Forbes magazine, in 2007, Duncan was the richest person in the city of Houston and the 3rd richest person in Texas, with a net worth of 8.2 billion dollars (according to page 46 in the October 27, 2008 issue of Forbes, Duncan's net worth dropped from 7.6 billion on Aug 29th to 6.3 billion on October 1) . He was worth 9.0 billion at the time of his death.

Duncan died aged 77 of a cerebral hemorrhage at his River Oaks, Houston home on March 28, 2010. Due to the repeal of the estate tax law for the year 2010, Duncan became the first American Billionaire to pay no estate tax since its enactment.