Vienna is the daughter of Rico Dredd and a woman named Fabienne Brown, a reporter who was interviewing him on Titan. After returning to Mega-City One Dredd had Vienna's mother arrested for fraternizing with a prisoner and charged with two years in prison, she was murdered there.
Vienna is the Niece of Judge Dredd, the two had a relationship when she was a child, with Dredd occasionally visiting her, but he decided to have nothing more to do with her and sent her away.
She later returned and they eventually managed to get back on good terms.
Vienna Dredd was created by John Wagner and Ian Gibson. Appearing in the Judge Dredd series of comic books, the character was first introduced in 1979, in 2000AD issue 116.