There is no harm in marrying the guy with your same blood group. Everyone is born with a certain blood type that is either Rh positive or Rh negative. Rh-positive blood is more common than Rh-negative. there is no problem for you to marry a partner with the same blood type/grouping as yourself.
When looking at a blood type, it is not the letter you should be concerned about, but the Rh factor (the positive or negative sign after your blood type letter, example: O + or O-). A woman is at risk when she has a negative Rh factor (example: O-) and her partner has a positive Rh factor (example: O +). This combination can produce a child who is Rh positive. While the mother's and baby's blood systems are separate there are times when the blood from the baby can enter into the mother's system. This can cause the mother to create antibodies against the Rh factor, thus treating an Rh positive baby like an intruder in her body. If this happens the mother is said to be sensitized.
A sensitized mother's body will make antibodies. These antibodies will then attack an Rh positive baby's blood, causing it to breaking down the red blood cells of the baby and anemia will develop. In severe cases this hemolytic disease can cause illness, brain damage.