Touting a "world exclusive," the tabloid's latest issue features California businessman Doug Gotterba boasting about an alleged gay relationship with Travolta.
The front page of the Enquirer shows what appears to be a nude Travolta swimming and a photo of Gotterba and the actor walking along a beach.
Gotterba, a former airline pilot, claims he met Travolta in 1981 and carried on a gay affair with the "Saturday Night Fever" actor until 1986.
The 61-year-old businessman, who said Travolta hired him as a pilot, alleged that he even remembers the exact date of when his sexual relationship with the actor began - Sept. 21, 1981.
"I know the date because I still have the log books and records," Gotterba said, according to the magazine.
The tabloid says it obtained a sex tape featuring Travolta and Gotterba along with a "private" photo album of the alleged gay lovers.
Rumors that Travolta is gay have dogged the actor for years.
Before Gotterba's claims, a pair of masseuses alleged Travolta inappropriately touched them during massages earlier this year. One of the massage specialists dropped their complaint.
The Enquirer noted Travolta's attorneys deny the gay rumors.