The fire broke out just after 6 p.m. at the Edge at Greentree Apartments in the 700 block of Appletree Court.
PHOTOS: Apartment building fire in Claymont
Flames were shooting from the second and third floors of the building when firefighters arrived.
A total of 22 units were damaged, with with damage estimated at $800,000.
No injuries were reported.
The fire was declared under control at 7:15 p.m.