[ecfisa]

Hola.

Usando for podrías hacer:

Código Delphi [-]
procedure TForm1.Button1Click(Sender: TObject);
var
  i,j: Integer;
begin
  with ListBox1 do
    for i:= 0 to Items.Count-1 do
      for j:= Items.Count-1 downto i+1 do
        if Items[i] = ListBox1.Items[j] then
          Items.Delete(j);
end;

Saludos.