I am holding dual citizenship and owns real properties here in the US. However, I am almost 60 years old and I am preparing my will. I want to designate my grand daughter as my trustee because I don't have children or husband.my concern is my grand daughter is not a US citizen and my question is will she be recognized by the US government as my trustee? Thank you.

The U.S. government probably will have nothing to do with it. It's a matter of state law, not federal. In what states is your property located?