Оформил: DeeCo
Автор: http://www.swissdelphicenter.ch

// Move item 1 after item 4 
// Bewege Item 1 hinter Item 4 

function MoveListViewItem(listView: TListView; ItemFrom, ItemTo: Word): Boolean;
 var
   Source, Target: TListItem;
 begin
   Result := False;
   listview.Items.BeginUpdate;
   try
     Source := listview.Items[ItemFrom];
     Target := listview.Items.Insert(ItemTo);
     Target.Assign(Source);
     Source.Free;
     Result := True;
   finally
     listview.Items.EndUpdate;
   end;
 end;

 procedure TForm1.Button1Click(Sender: TObject);
 begin
   // Listview1.ViewStyle := vsReport; 
  if MoveListViewItem(Listview1, 1, 4) then
     ShowMessage('Moved!');
 end;