The black J-31 rose in a nearly vertical climb on take-off in Zhuhai before circling back and doing two rolls, in the aircraft's first announced public appearance.
The plane's existence has been the subject of rumour and speculation for years, with photographs appearing increasingly frequently on military websites in recent months.
Defence analysts say the J-31 is China's answer to the United States' F-35, though the Chinese jet lags behind the American one technologically.
The fighter's Chinese name is "Falcon Eagle" and it is manufactured by a unit of Aviation Industry Corp. Of China (AVIC), whose defence arm uses the slogan: "We are making the best weapons for guardians of the peace."
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China's air force said the display of military might at the airshow showed the intention to build a strong country.
The People's Liberation Army (PLA) air force "will make unremitting efforts to realise dreams of a strong China and powerful armed forces", read a sign alongside an array of eight warplanes at the airshow.
"The display... Demonstrates the strength and confidence of (the) PLA Air Force to fulfil missions and achieve world peace."