No, a woman can't have her menstrual period while she is pregnant. Some women may, however, have vaginal bleeding during pregnancy, which can be confused with menstrual bleeding. Menstruation only happens when you are not pregnant.
Each month, the uterine lining (endometrium) grows to prepare for an egg to embed there. If pregnancy does not occur, the woman sheds this tissue and bleeds, and that is what we know as menstrual period.