.....
Data := VarArrayCreate([1, AGrid1.RowCount, 1, AGrid1.ColCount], varVariant);
  for i := 0 to AGrid1.ColCount - 1 do
    for j := 0 to AGrid1.RowCount - 1 do
      Data[j + 1, i + 1] := AGrid1.Cells[i, j];

Sheet.Range[RefToCell(1, 1), RefToCell(AGrid1.RowCount + 4 (Это смещение. Да?) ,
      AGrid1.ColCount)].Value := Data;

....

function RefToCell(ARow, ACol: Integer): string;
begin
  Result := Chr(Ord('A') + ACol - 1) + IntToStr(ARow);
end;

function SaveAsExcelFile(AGrid: TStringGrid; ASheetName, AFileName: string): Boolean;
const
  xlWBATWorksheet = -4167;
var
  Row, Col: Integer;
  GridPrevFile: string;
  XLApp, Sheet, Data: OLEVariant;
  i, j: Integer;
begin
  // Prepare Data
  Data := VarArrayCreate([1, AGrid.RowCount, 1, AGrid.ColCount], varVariant);
  for i := 0 to AGrid.ColCount - 1 do
    for j := 0 to AGrid.RowCount - 1 do
      Data[j + 1, i + 1] := AGrid.Cells[i, j];
  // Create Excel-OLE Object
  Result := False;
  XLApp := CreateOleObject('Excel.Application');
  try
    // Hide Excel
    XLApp.Visible := False;
    // Add new Workbook
    XLApp.Workbooks.Add(xlWBatWorkSheet);
    Sheet := XLApp.Workbooks[1].WorkSheets[1];
    Sheet.Name := ASheetName;
    // Fill up the sheet
    Sheet.Range[RefToCell(1, 1), RefToCell(AGrid.RowCount,
      AGrid.ColCount)].Value := Data;
    // Save Excel Worksheet
    try
      XLApp.Workbooks[1].SaveAs(AFileName);
      Result := True;
    except
      // Error ?
    end;
  finally
    // Quit Excel
    if not VarIsEmpty(XLApp) then
    begin
      XLApp.DisplayAlerts := False;
      XLApp.Quit;
      XLAPP := Unassigned;
      Sheet := Unassigned;
    end;
  end;
end;