Karen Rodger, 41, and her husband Colin, 44, were "over the moon" to welcome Rowan and Isla into their family at the Southern General Hospital in Glasgow, British newspaper 'Metro' reported.
Rowan and Isla were her first girls after having two sets of boys.
The couple have four boys - 14-year-olds Lewis and Kyle and Finn and Jude who are both 12 - and were told of the unlikely odds that Karen's third pregnancy would be twins.
The chances of couple having three sets of twins was 1 in 500,000.
Karen said: "I just could not believe it. It never crossed my mind that it would be twins again."
She said she is "excited" by a family of six children.
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