Claire Hatch, 27, from Southampton, was on the gravity swing at Hangloose Adventures while she was on holiday in Cornwall.
She said: "It was only me being yanked backwards that saved me from being very seriously hurt, or worse."
A spokesman at Hangloose Adventures apologised for "the regrettable accident".
The Eden Project said that the swing was operated by a separate company, and it was "upset to learn about the accident".
Ms Hatch was two days into her holiday when she went on the swing with her nine-year-old son.
Her partner Richard Dawkins, 47, who filmed the incident, said a rope which was used to start the swing was left dangling in Ms Hatch's face when it "wrapped around her throat".
He said: "It could have been fatal. We just want to know that everything has been done to prevent it happening again."
Posting on her Facebook page, she said: "I would really like to point out that the safety checks and on site medical facilities need to be better."
Ms Hatch was treated for her injuries at the Royal Cornwall Hospital near Truro and released on the same day.
A spokesman at Hangloose Adventures Ltd said: "We apologise for the distress caused to Claire Hatch as a result of the regrettable recent accident on Gravity the giant swing were she received a rope burn to her neck.
"As a result of the incident, we have reviewed the design of the swing's release mechanism, our standard operating procedures and our staff training."
A woman suffered a rope burn to her neck in a safety failure while she was on a giant swing at the Eden Project.