It is the first time the Liaoning has been deployed to "distant sea waters", state media report.
Details of the location, route or duration of the drill have not been given.
The exercise comes amid renewed tension over self-ruled Taiwan, which Beijing sees as a breakaway province.
"A Chinese navy formation, including the aircraft carrier Liaoning, headed towards the West Pacific on Saturday for scheduled blue-water training," Chinese state news agency Xinhua reported, quoting navy spokesperson Liang Yang.
Taiwan's defence ministry said it had been monitoring the drills closely as the Liaoning went through the Miyako Strait, a body of water between the Japanese islands of Miyako and Okinawa, heading into the Pacific, Reuters news agency reported.
Japan's defence ministry said it spotted the Liaoning as part of a fleet of eight Chinese warships that included destroyers and frigates, in the central part of the East China Sea.
It said there was no incursion into Japanese waters.
China announced the Liaoning was ready to engage in combat in November, marking a milestone for a navy that has invested heavily in its ability to project power around the region.
But China is still years away from perfecting carrier operations similar to those the United States has practiced for decades, according to Reuters.
Earlier this month, the Liaoning conducted live-fire drills for the first time in the Bohai Sea, near the Korean peninsula.
China's increasing military presence, in the South China Sea in particular, where it has territorial disputes with several neighbours, has fuelled concern.
The Western Pacific exercise comes amid new tension over Taiwan, following US President-elect Donald Trump's telephone call with the island's president that upset China.