Is it possible to change person's blood group?
I know it is not possible to change person's DNA, so what about blood group?
Yes, it is possible. In a bone marrow transplant, all of the patient's bone marrow is destroyed and replaced with donor marrow. Since red blood cells are created by bone marrow, the donor's blood type will determine which type of red cells are produced, as explained here:
Does my blood type change after SCT or BMT?
Yes. The recipients blood type eventually changes to the donor type. That means if you had a blood type of A+ prior to transplant and your donor had a blood type of O, eventually your blood type would become O. I may take several weeks, possibly months for your original blood type to disappear, but eventually it will.
There is also one report of an Australian girl whose blood type changed following a liver transplant. That appears to have been a unique event, but it does indicate that it is possible by means other than marrow transplant.