Officers responded around 7:50 Sunday night to a call in the area of 25th and Thatcher Street regarding an assault.
On the scene, they found an unresponsive 37-year-old woman lying on the sidewalk with severe injuries to her head.
The victim transported to Christiana Hospital where she remains in serious condition.
Wilmington detectives and Maryland police arrested her ex-boyfriend Gregory Griffin without incident in Elkton, Maryland at a relative's house. He is charged with attempted murder and endangering the welfare of a child, since the victim's children were present during part of the assault.