The tests included a fighter launch and air combat and recovery exercises, AP reports.
The next steps for the Liaoning carrier group will be "cross-sea" training and tests at an unspecified location. Chinese media are speculating that this could mean the ships will conduct operations in areas of the contested South China Sea.
AP quotes a military analyst in China's Global Times newspaper as saying the South China Sea would be an "ideal" location because joint exercises could be done in areas controlled by China.
The South China Sea is a patchwork of contention right now, with Brunei, China, Indonesia, the Philippines, Taiwan and Vietnam all involved in territorial disputes in the area. China claims nearly all of the sea and this week launched daily civil charter flights to Woody Island, an island in the Parcels group that is also claimed by Taiwan and Vietnam.
The US and China have accused the other of escalating a military buildup in the region, with China calling its military installations "defensive" while accusing the US of making provocative passes nearby. China seized an unmanned underwater US Navy drone last week, leading to days of tension compounded by US President-elect Donald Trump's tweets about the incident, which he called an "unprecedented attack." China returned the drone soon after nabbing it, though Trump also said they should "keep it."
Trump has previously antagonized China by suggesting the country made up climate change as a way to remain an industrial leader, and by taking a phone call from the President of Taiwan, which China also claims.
The Liaoning was declared combat-ready last month and held its first live-fire exercises last week.