// Move item 1 after 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;