Bornean orangutan Tatau was born at the zoo in April, but has now been on public display. She has been raised naturally by her mother Mali, one of five orangutans at the zoo.
Zoo spokesman Philip Knowling told the Plymouth Herald: "Mali has been such a good mother. She just quietly gets on with it. It is the best thing in the world for a mother to rear their young naturally.
"Hand rearing from our point of view is the less good option because it can affect how the animal might behave when they are older."
She has been pictured cuddling up to mum, as well as swinging and chewing on ropes.
The Bornean orangutan is a species of orangutan native to the island of Borneo. Together with the Sumatran orangutan, it belongs to the only genus of great apes native to Asia.
Like the other great apes, orangutans are highly intelligent, displaying advanced tool use and distinct cultural patterns in the wild. Orangutans share approximately 97% of their DNA with humans.
The Bornean orangutan is an endangered species, with deforestation, palm oil plantations and hunting posing a serious threat to its continued existence.
Baby zoo animals around the world
Pictures: Baby orangutan delighting visitors at Paignton Zoo
These babies, named Sri Kandi (left) and Arjuna (right) were born at Tierpark, Berlin, Germany. They made their debut on 5 March 2012.
Clinging to his mum, baby Changi meets his public for the first time at Krefeld Zoo, Germany.
This little rhino, named Male, was born in January. He's pictured here with his mother, Mana, at Magdeburg Zoo, Germany.
The zoo at Tierpark in Berlin celebrated the birth of a litter of four dingo babies in January.
Only a few days old, this baby giraffe, named Kimarle, peaks out from her enclosure at the ZOOM Zoo in Gelsenkirchen, western Germany. The 170cm tall giraffe was born on March 9.
A one-month-old baby squirrel monkey clings to its mother's back at Qingdao Forest Wildlife Park, China.
A two-week old baby gorilla is cuddled by her mum, Mumba, a Western Lowland Gorilla, at Port Lympne Wild Animal Park near Ashford, Kent.
Born at Cincinnati Zoo, US, this one-month old hedgehog is being hand reared by keepers until it is old enough to be included in the zoo's outreach programme.
Ludwig the baby elephant is clearly happy to be out and about at the Tierpark Hellabrunn Zoo, Munich.
These cuties were born in February at Bristol Zoo Gardens.
This cub was born prematurely at Toronto Zoo. His mum rejected him soon after he was born, so he was cared for by staff at the zoo. Here he is making his debut in February.
This six-month old baby Western Lowland Gorilla is seen here enjoying the spring sunshine with her mother at Dublin Zoo.