The U-boat was laid down on 9 July 1944 at the Schichau-Werke yard at Danzig, launched on 25 August 1944, and commissioned on 7 October 1944 under the command of Oberleutnant zur See Horst Willner.

Her commander, Captain Horst Willner, disguised his wife as a sailor and smuggled her aboard together with their three-month-old baby (a crime punishable by death).

The captain's family was originally to be evacuated on MV Wilhelm Gustloff, joining a flood of refugees fleeing East Prussia ahead of the advancing Red Army, in "Operation Hannibal".

The refugees, including the captain's family, were safely delivered at Travemünde, Lübeck on 2 April 1945.

Returning to Kiel, U-3505 was to participate in torpedo exercises, but on 3 April was sunk in a bombing raid while in harbour.