The Defense Ministry said the drills started Monday at 0530 gmt from this tiny enclave of fishing communities and military bases only about seven miles (11 kilometers) from North Korean shores.
The North shelled the island on Nov. 23 after similar drills, killing two marines and two civilians.
The North considers the waters around Yeonpyeong its own territory and has threatened to retaliate for any new drills.
South Korea's military said ahead of Monday's drills that it will "immediately and sternly" deal with any North Korean provocation.
South Korea ordered residents of front-line islands into bomb shelters. An Associated Press Television News cameraman heard the sounds of explosions Monday afternoon.
U.N. diplomats meeting in New York failed to find any solution to ease fears of a new war on the Korean peninsula, nearly a month after the North shelled South Korea's Yeonpyeong Island in retaliation for earlier artillery exercises there. The North has said it would respond even more harshly to any new drills from the Yellow Sea island.
South Korea's new drills from Yeonpyeong brought tensions to their highest point since the North's Nov. 23 bombardment, which was the North's first attack targeting civilian areas since the 1950-53 Korean War.
Residents, local officials and journalists Yeonpyeong and four other islands were ordered to evacuate to underground shelters because of possible attacks by North Korea, Ongjin County government spokesman Won Ji-young said.