Rob Griffiths, 44, and three of his four children-Rhys, 20, Rhiann, five, and Nelly, two-suffer from a genetic defect that can cause "sudden death syndrome".
Long QT, which is thought to affect just one in 5,000 people, is one condition in which otherwise fit and healthy people may suffer fatal heart failure.
According to reports, Rhys was the first member of the family to be diagnosed, at the age of 15, after he collapsed while on holiday.
The rest of the family were also tested, given the genetic nature of the condition.
Rob, from North Wootton in Norfolk, knows that the condition could completely shut down his heart.
"It would be just like a power cut of the electrical supply to the heart," the Telegraph quoted him as saying.
He, however, insisted that he wanted to make life as normal as possible for his children.
"You can't wrap them in cotton wool or never let them out. Yes, they've got a condition but that's not the life we want them to have. Rhiann tells everyone she has a special heart," he said.
The Griffiths family take stress-relieving heart medication Beta Blockers every night, and have regular check ups with their doctor.
Alison Cox, from the charity Cardiac Risk in the Young (CRY), said that the condition could have a very "horrific" impact.
"With a terminal illness the family has time to prepare and are able to say their goodbyes. But with Long QT the person is either fit and healthy, or suddenly dead," she said.