uses
  IniFiles;

procedure TForm1.Button1Click(Sender: TObject);
var
  I: Integer;
  AppIni: TMemIniFile;
begin
  AppIni := TMemIniFile.Create(ExtractFilePath(Application.ExeName) + 'Test.ini', TEncoding.UTF8);
  try
    for I := StringGrid1.FixedRows to StringGrid1.RowCount - 1 do
    begin
      StringGrid1.Cells[0, I] := AppIni.ReadString('Column1', 'Row' + IntToStr(I), '');
      StringGrid1.Cells[1, I] := AppIni.ReadString('Column2', 'Row' + IntToStr(I), '');
    end;
  finally
    AppIni.Free;
  end;
end;