Annie Gladstone, 21, had her first set of twins - Lillie and Jayden - four years ago, and her second set are due in September.
The Royal College of Midwives said Annie is the youngest person to have two sets of twins.
Annie and her fiancé Rich Porter, 26, were not expecting to have one - let alone two - sets of twins, as multiple births don't run in either of their families.
"When the nurse told us we were shocked," said Annie, who conceived both sets of twins naturally. "You could have heard a pin drop.
"It took about a minute for me to begin breathing, and Rich's face went so pale. But after the initial shock, of course we are delighted.
"We've been told we're having girls, so Rich and Jayden are definitely about to get very outnumbered at home.
"They say your second baby is easier to cope with than your first, but since our first and second came at the same time, we're hoping babies three and four are a breeze."
Annie's second pregnancy hasn't been all plain sailing. She's suffering from chronic SPD (Symphysis Pubis Dysfunction) - pelvic pain caused by the stress of carrying babies. During the later stages of her pregnancy she may have to use crutches to get around.
She says the condition is 'horrible' and she's in constant pain, but it will clear up once her babies are born.
"I always wanted kids. We both did," she adds. "But we never wanted a big family. Last year I said to Rich that I wanted another baby, and then we'd stop. I guess good things come in twos."
Jacque Gerrard, director for England at the Royal College of Midwives, said: "I have been a midwife for over 30 years and have never seen someone at such a young age have two sets of twins in succession like this.
"As a mother of twins myself I know what she is going through and I wish her well in her pregnancy.
"'The experience gained with her first set of twins will be helpful when she gives birth second time round."
Tennis champ Roger Federer and his wife Mirka welcomed their second sets of twins earlier this year.
Good luck, Annie!
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