Delete row in StringGrid- Delphi

I want to make something like that. I have a list in my StringGrid and i want to delete one row by selecting cell and then clicking the button. Then this list should show again in StringGrid without this row. The biggest problem i have with deleting row, i tried whis one procedure but it only deleted row in StringGrid, not in list, i think.

    procedure DeleteRow(Grid: TStringGrid; ARow: Integer);
var
  i: Integer;
begin
  for i := ARow to Grid.RowCount - 2 do
    Grid.Rows[i].Assign(Grid.Rows[i + 1]);
  Grid.RowCount := Grid.RowCount - 1;
end;

Please someone for help. :)

The selected row can be retrieved StringGrid1.selected and the you can call the following procedure.

procedure TUtils.DeleteRow(ARowIndex: Integer; AGrid: TStringGrid);
var
  i, j: Integer;
begin
  with AGrid do
  begin
    if (ARowIndex = RowCount) then
      RowCount := RowCount - 1
    else
    begin
      for i := ARowIndex to RowCount do
        for j := 0 to ColumnCount do
          Cells[j, i] := Cells[j, i + 1];

      RowCount := RowCount - 1;
    end;
  end;
end;