No one was injured in the overnight attack, the second on the agency's offices this week, police said on Friday.
It was not clear who threw the grenades. Supporters of caretaker Prime Minister Yingluck Shinawatra have been demonstrating at the building this week.
The NACC is examining the alleged failure of Ms Yingluck to stop corruption and stem huge losses in the government's flagship rice-buying programme.
It is widely expected to recommend her impeachment by the Senate. If the Senate takes up the case, Yingluck will have to step aside, with a deputy prime minister expected to take over. If she is found guilty by the Senate, she has to step down.
Her supporters, who have been restrained during five months of anti-government protests in the capital, are starting to mobilise and are planning their own big rally, or series of rallies, on April 5.
Anti-government demonstrators resumed street protests on Monday after lying low for weeks. Their rally this Saturday is expected to draw up to 50,000 people, according to Paradorn Pattanathabutr, a security adviser to the prime minister.
"We don't expect any violence at the rally but provocateurs might try to stir trouble to discredit the government side," Lt Gen Paradorn said.