procedure FitGrid(Grid: TDBGrid);
const
  C_Add=3;
var
  ds: TDataSet;
  bm: TBookmark;
  i: Integer;
  w: Integer;
  a: Array of Integer;
begin
  ds := Grid.DataSource.DataSet;
  if Assigned(ds) then
  begin
    ds.DisableControls;
    bm := ds.GetBookmark;
    try
      ds.First;
      SetLength(a,Grid.Columns.Count);
      while not ds.Eof do
      begin
        for I := 0 to Grid.Columns.Count - 1 do
        begin
          if Assigned(Grid.Columns[i].Field) then
          begin
            w :=  Grid.Canvas.TextWidth(ds.FieldByName(Grid.Columns[i].Field.FieldName).DisplayText);
            if a[i] < w  then
               a[i] := w ;
          end;
        end;
        ds.Next;
      end;
      for I := 0 to Grid.Columns.Count - 1 do
        Grid.Columns[i].Width := a[i] + C_Add;
        ds.GotoBookmark(bm);
    finally
      ds.FreeBookmark(bm);
      ds.EnableControls;
    end;
  end;
end;

procedure TForm1.Button1Click(Sender: TObject);
begin
  FitGrid(DBgrid1)
end;