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

// Move an item up 

procedure LbMoveItemUp(AListBox: TListBox);
 var
   CurrIndex: Integer;
 begin
   with AListBox do
     if ItemIndex > 0 then
     begin
       CurrIndex := ItemIndex;
       Items.Move(ItemIndex, (CurrIndex - 1));
       ItemIndex := CurrIndex - 1;
     end;
 end;

 procedure TForm1.Button1Click(Sender: TObject);
 begin
   LbMoveItemUp(ListBox1);
 end;

 // Move an item down 

procedure LbMoveItemDown(AListBox: TListBox);
 var
   CurrIndex, LastIndex: Integer;
 begin
   with AListBox do
   begin
     CurrIndex := ItemIndex;
     LastIndex := Items.Count;
     if ItemIndex <> -1 then
     begin
       if CurrIndex + 1 < LastIndex then
       begin
         Items.Move(ItemIndex, (CurrIndex + 1));
         ItemIndex := CurrIndex + 1;
       end;
     end;
   end;
 end;

 procedure TForm1.Button2Click(Sender: TObject);
 begin
   LbMoveItemDown(ListBox1);
 end;