uses
    Math;
function DBGridRecordSize(mColumn: TColumn): Boolean;
begin
    Result := False;
    if not Assigned(mColumn.Field) then
        Exit;
    mColumn.Field.Tag := Max(mColumn.Field.Tag, TDBGrid(mColumn.Grid).Canvas.TextWidth(mColumn.Field.DisplayText));
    Result := True;
end; 
function DBGridAutoSize(mDBGrid: TDBGrid; mOffset: Integer = 5): Boolean;
var
    I: Integer;
begin
    Result := False;
    if not Assigned(mDBGrid) then
        Exit;
    if not Assigned(mDBGrid.DataSource) then
        Exit;
    if not Assigned(mDBGrid.DataSource.DataSet) then
        Exit;
    if not mDBGrid.DataSource.DataSet.Active then
        Exit;
    for I := 0 to mDBGrid.Columns.Count - 1 do
    begin
        if not mDBGrid.Columns[I].Visible then
            Continue;
        if Assigned(mDBGrid.Columns[I].Field) then
            mDBGrid.Columns[I].Width := Max(mDBGrid.Columns[I].Field.Tag,
                mDBGrid.Canvas.TextWidth(mDBGrid.Columns[I].Title.Caption)) + mOffset
        else
            mDBGrid.Columns[I].Width := mDBGrid.Canvas.TextWidth(mDBGrid.Columns[I].Title.Caption) + mOffset;
        mDBGrid.Refresh;
    end;
    Result := True;
end; 
procedure TForm1.DBGrid1DrawColumnCell(Sender: TObject; const Rect: TRect; DataCol: Integer; Column: TColumn;
    State: TGridDrawState);
begin
    DBGridRecordSize(Column);
end;
procedure TForm1.Button1Click(Sender: TObject);
begin
    DBGridAutoSize(DBGrid1);
end;