The yet-to-be-christened Type 001A carrier left a shipyard at the northeastern port of Dalian at 6.45am, Xinhua said, and sailed out of the port half an hour later.
The sea trials will mainly test the reliability and stability of the carrier's power system and other equipment.
The new warship is an upgrade to the Liaoning, China's only operational aircraft carrier, a retrofitted Soviet-era Admiral Kuznetsov-class multi-role vessel.
Military observers have been watching for signs the new aircraft carrier was about to start sea trials after photos of it being moved from its berth by tugboats were published by state media on April 23.
The 65, ooo-ton Type 001A carrier was launched at the DSIC shipyard in April 2017.
Sam Roggeveen, senior fellow at Sydney's Lowy Institute, said: 'This is, in and of itself, not created to be some frontal challenge to United States power in the Asia Pacific, because it simply isn't in the class of America's aircraft carriers'.
The new aircraft carrier has an inclined ramp and can accommodate more aircraft than its predecessor.
The US is the largest operator as it runs 11 nuclear-powered carriers with each having a full-load displacement of about 100,000 tonnes. China a year ago established its first overseas military base in the Horn of Africa nation of Djibouti, where rivals such as the U.S., Japan and several European nations also have a permanent presence.
The Shandong will be able to carry up to 24 Shenyang J-15 multirole fighter jets, a variant of the fourth-generation Sukhoi Su-33 twin-engines air superiority fighter, as well as around ten rotary wing aircraft including Changshe Z-18, Ka-31, or Harbin Z-9 helicopters.
China has sent its first home-built aircraft carrier for sea trials as the Communist government attempts to assert its military might on the world stage. The ship's chief engineering commander, Hu Wenming, told the broadcaster the carrier was smaller than US carriers' Nimitz class.
The vessel has more than 3,600 cabins.
Officials of the Navy said, several aspects of the new carrier are different from those on the Liaoning.
This is unedited, unformatted feed from the Press Trust of India wire.