The first pair of female twins was born to nine-year-old Qiyuan, or Magic Luck, at a panda breeding research center in the provincial capital of Chengdu, the Xinhua news agency said.
More than an hour later, eight-year-old Chenggong, or Success, gave birth to another cub, followed by eight-year-old Zhuzhu, or Pearl, who delivered early on Sunday morning.
China has 239 giant pandas in captivity. There are also nearly 1,600 living in the wild in the country, mostly in Sichuan and neighboring provinces.
Large areas of the bamboo forests that provide shelter and food for pandas in southwest China's Sichuan province were buried under debris and landslides caused by the recent earthquake in the region.
A total of 54 pandas were evacuated from the world-famous Wolong panda reserve after the most powerful earthquake for 30 years hit Sichuan on May 12. Some 70,000 people died in the quake.
Beijing has often presented giant pandas to foreign countries as a way of signifying good relations. The practice, sometimes called 'panda diplomacy,' has existed since the Tang Dynasty, when a pair of pandas was sent by a Chinese empress to a Japanese emperor.