The network said: “TNT has decided not to renew Dallas”, adding it “defied expectations by standing as a worthy continuation of the Ewing saga”.
TNT thanked “everyone involved in the show” and the people of Dallas “for their warm and generous hospitality”.
The series followed the fortunes of Texan oil family the Ewings.
The original Dallas aired from 1978 to 1991 and centered on a long and bitter rivalry between brothers JR Ewing, played by Larry Hagman, and Bobby Ewing, played by Patrick Duffy.
It began as a mini series in 1978 and went on to become one of the most-watched television shows around the world for 13 years.
The 356 episodes were seen by an estimated 300 million people in 57 countries.
The new version followed the power struggles within two feuding Texan oil and cattle-ranching families, focusing on John Ross and Christopher Ewing as they clashed over the future of the family dynasty.
Josh Henderson, who appeared as a child in the original series, played John Ross, son of JR Ewing, while Desperate Housewives star Jesse Metcalfe was Christopher, son of Bobby Ewing.
Original cast members Larry Hagman, Patrick Duffy and Linda Gray also returned to Southfork ranch as JR, Bobby and Sue Ellen.
In November 2012 Larry Hagman died at the age of 81 from cancer and cirrhosis of the liver.
The series was rewritten to reflect this, incorporating his death into the storyline.
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