Unusually the mother gave birth during the day which allowed keepers to film it. She (Sangha) had been regnant for around 14 months.
The birth was important as Rothschild's Giraffe are the most endangered of all the giraffe species.
The baby's father is a 10 year old called Yoda. Sangha and her breeding partner Yoda had another calf, a male, in August last year but it died shortly after birth.
The baby was born six foot tall and was running around within hours.
There are only 670 Rothschild's giraffes in the world, making them rare than Giant Pandas.
This unnamed female Rothschild's Giraffe was born at Paignton Zoo in Devon on Saturday.