A former US Navy SEAL who wrote a best-selling book about his experiences as a sniper has been fatally shot along with another man on a Texas gun range.

American Sniper author Chris Kyle, 38, and a second man were found dead at Rough Creek Lodge's shooting range in Glen Rose, Erath County Sheriff Tommy Bryant said.

Witnesses said a gunman opened fire on the men, then fled in a pickup truck belonging to one of the victims, according to the Star-Telegram.

The newspapers said a 25-year-old man was later taken into custody in Lancaster, southeast of Dallas, and that charges were expected.

Glen Rose is about 128km southwest of Dallas.

Mr Kyle wrote the best-selling book American Sniper: The Autobiography of the Most Lethal Sniper in U.S. Military History, detailing his 150-plus kills of insurgents from 1999 to 2009.

Investigators did not immediately release the name of the second victim.

Mr Kyle was sued by former Minnesota Governer and ex-professional wrestler Jesse Ventura over a portion of the book that claims Mr Kyle punched Ventura in a 2006 bar fight over unpatriotic remarks.

Mr Ventura says the punch never happened and that the claim by Mr Kyle defamed him.

Mr Kyle had asked that Mr Ventura's claims of invasion of privacy and "unjust enrichment" be dismissed, saying there was no legal basis for them.

However, a federal judge said the lawsuit should proceed. Both sides were told to be ready for trial by 1 August.