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StartingPoint : TPoint;

procedure TForm1.FormCreate(Sender: TObject) ;
begin
ListBox1.DragMode := dmAutomatic;
end;

procedure TForm1.ListBox1DragDrop(Sender, Source: TObject; X, Y: Integer) ;
var
DropPosition, StartPosition: Integer;
DropPoint: TPoint;
begin
DropPoint.X := X;
DropPoint.Y := Y;
with Source as TListBox do
begin
StartPosition := ItemAtPos(StartingPoint,True) ;
DropPosition := ItemAtPos(DropPoint,True) ;
Items.Move(StartPosition, DropPosition) ;
end;
end;

procedure TForm1.ListBox1DragOver(Sender, Source: TObject; X, Y: Integer; State: TDragState; var Accept: Boolean) ;
begin
Accept := Source = ListBox1;
end;

procedure TForm1.ListBox1MouseDown(Sender: TObject; Button: TMouseButton; Shift: TShiftState; X, Y: Integer) ;
begin
StartingPoint.X := X;
StartingPoint.Y := Y;
end;