月份减一月情况：

function GetLastMonth(ADate : TDateTime) : TDateTime;
var
  dwYear, dwMonth, dwDay : Word;
begin
  Result := ADate;
  Try
    DeCodeDate(ADate, dwYear, dwMonth, dwDay);
    Result := EncodeDate(dwYear, dwMonth, 1) - 1;
  except
  end;
end

月份增加一月情况：

function TForm1.GetLastMonth(ADate: TDateTime): TDateTime;
var
  dwYear, dwMonth, dwDay : Word;
begin
  Result := ADate;
  Try
    DeCodeDate(ADate, dwYear, dwMonth, dwDay);
    if dwMonth=12   then
    begin
    Result := EncodeDate(dwYear+1, 1, 1);
    end
    else
    Result := EncodeDate(dwYear, dwMonth+1, 1);
  except
  end;
end;

调用：

Edit1.Text:=DateTimeToStr(GetLastMonth(Date()));