I assume this is a grandson you have acquired through a second relationship formed by one of your children.
If it was a genuine grandson (i.e. a son of your child) they would be first cousins, once removed (that is, your great grandson would be the child of your grandson's cousin). But as things are I cannot see a relationship other than “step-first-cousins-once-removed” which sounds a bit of a mouthful, not to say silly!
My Step Grandson is the son of my Step daughter.
My Great Grandson is the son of my Grandson.
Agree that "step-first-cousins-once removed" is a bit of a mouthful.
What is also interesting (but not relevant) both were born within 7 days of each other 4 months ago.
Sorry, Penelope, I misunderstood how you “acquired” your step grandson.
Without the “step” complication your grandson would indeed be uncle to your great grandson. I don’t know if “step uncle” is a recognised term but Tuvok’s suggestion seems to fit the bill as well as anything I can come up with.