"After several months of preparations, the summer exercise of the People's Liberation Army (PLA) began," said the Hong Kong-based Ta Kung Pao newspaper.
It said the exercise started "in the first 10 days of this month" and were expected to last a week.
China has said it would use the joint sea, land and air drills to demonstrate its ability to dominate air space over Taiwan, an essential element in any invasion.
The newspaper, citing military experts, repeated that this was a key element of the mission.
"18,000 soldiers are participating in the exercise. The objective of the exercise this time is to fight to control air space over Taiwan," it said.
Previous state media reports have said practically all the advanced weaponry China possesses would be used in the exercise, including Sukhoi Su-27 fighter jets purchased from Russia.
Nuclear-powered submarines, warships, the latest model missile destroyers and a guided missile brigade would also reportedly be involved.
The Ta Kung Pao said the war games were intended to "show to Taiwan independence forces that if they go ahead, one day the PLA is confident and capable of resolving the Taiwan issue".
The drills are taking place on Dongshan Island in southeastern China's Fujian province, just 150 nautical miles west of Taiwan's Penghu Island.
Tension between Beijing and Taipei has been heightened since Taiwanese President Chen Shui-bian was re-elected this year, with China fearful his pro-independence moves were aimed at gaining formal independence.
Beijing has vowed to go to war with Taiwan in the event of it moving towards independence.
Another Hong Kong-based pro-Beijing paper, the Wen Wei Po, said Thursday that Beijing has given Taiwan 20 years to come back into the Chinese fold or face military action.
Unidentified sources were quoted as saying former Chinese president and Central Military Commission chairman Jiang Zemin had recently discussed a timetable regarding using force to achieve Taiwan's reunification in a speech at a military conference in Beijing.
Beijing has regarded Taiwan as a renegade province that must be reunified with China, by force if necessary, since the Communists won a civil war and drove the defeated Nationalists into exile on the island in 1949.