Normally, no. However, some women still experience their menstrual cycle while pregnant. If this happens, you should see your doctor as soon as possible.
In some pregnancies, 2 to 3 weeks after your last period, you can experience what's known as implantation bleeding. This is not menstrual bleeding, but can be mistaken for it.
It is very rare, I experienced spotting every month or so, it was just spotting. In the rare occasion that you do experience a high volume of bleeding during pregnancy; you must tell your OB/GYN and keep all your appointments. Ultrasounds are perhaps recommended to make sure your baby is all right. I got 5 ultrasounds throughout my last pregnancy due to the spotting. My son is now 3 years old, I wish you well.