The late-night blasts struck the base in Tarmiyah, a predominantly Sunni Arab town about 45 kilometres (30 miles) from the capital.
The first explosion was set off by a suicide bomber who detonated a vehicle rigged with explosives at the gate of the base, followed by another attacker who managed to enter the base before detonating his car.
In addition to the dead, at least 39 people were wounded.
The violence was the latest in the country's worst bloodshed since 2008, with more than 5,500 people dead so far this year, spurring Iraqi Prime Minister Nuri al-Maliki to appeal for greater cooperation with Washington to combat militancy.