Xinhua News Agency said Eryatou just gave birth to two female cubs at the Chengdu giant panda breeding centre in Sichuan province.
Earlier Jiaozi gave birth to a male and a female at the same facility.
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Mouthful: Twelve-year-old panda Jiaozi plays with one of her twin cubs
Getting to know you: A newborn cries under mum's watchful eye
Chinese panda breeding centres, which use artificial insemination techniques, have produced 14 cubs so far this year.
Last year 34 pandas were born in captivity, 30 of which survived.
The panda is one of the world's rarest animals, with an estimated 1,590 living in the wild while another 210 have been successfully bred in captivity.
A wild giant panda's diet is almost exclusively (99 percent) bamboo, which has been theatened by human habitation with farming destroying a lot of their food source.
Pandas also face threats to their own survival from their slow breeding and low birth rates.
Giant pandas reach breeding maturity between four and eight years of age and can reproduce about they are about 20 years old.
However, females ovulate only once a year and only have a short period of two to three days in which to conceive.
In the wild offspring stay with their mothers from one and a half to three years