Two loud blasts were heard in the area, known as the "Green Zone", on Thursday. It's thought both of the explosions were caused by suicide bombers.
The blasts happened at a popular cafe and a souvenir market.
There have been several attacks on the area by rebel fighters who are against the way Iraq is now being governed.
US officials said none of the people who died were soldiers or police officers.
They added that two of the people killed were American, but the nationalities of the other five are not yet known.
Iraq: picture galleries
Chat about the news
Try the Iraq quiz
