On Wikipedia, if you look at the profile of Gellert Grindelwald, then you can see that the blood status says 'half-blood or pure-blood'. Can anyone possibly give a more definite answer as to what blood status he has?
It's difficult to find out anything about Grindelwald, as there is very little information about Gellert Grindelwald's past. However, by some evidence, it can well be concluded that he was in-fact a pure blood. Let me put forth some of the theories based on existing information.
The only mention about Grindelwald's family member (is in the HP:Deathly Hallows) that Bathilda Bagshot, (the historian and author) was his great aunt. And according to here, she was a pure-blood witch. By this we can at least say that one side of his family tree was wizard-blood.
Going ahead, Grindelwald's studied at the Durmstrang Institute of Wizardry, which was well-known for its tolerance towards the Dark Arts. He was later suspended because even the likes of Durmstrang couldn't tolerate his level of crazy. To quote HPWikia here,
Grindelwald was expelled for twisted, dark experiments and near-fatal attacks on his fellow students.
Durmstrang, as well as its known for its tolerance towards the dark arts, it could also be rigid in admitting Muggle-borns or half-bloods. To quote Draco Malfoy in The Goblet of Fire,
"Father actually considered sending me to Durmstrang rather than Hogwarts, you know. He knows the Headmaster, you see. Well, you know his opinion of Dumbledore — the man's such a Mudblood-lover — and Durmstrang doesn't admit that sort of riff-raff. But Mother didn't like the idea of me going to school so far away, Father says Durmstrang takes a far more sensible line than Hogwarts about the Dark Arts. Durmstrang students actually learn them, not just the defence rubbish we do..."
Draco may well be referring to the Muggle-borns when he says 'riff-raff'. But it could also mean that he could be talking about everyone except the pure-bloods in general.
Here, on HP discussion, many reasons have been presented that indicate Durmstrang being a school that only admits pure-bloods. Thus, in my speculation, Gellert Grindelwald may well be one of them, (i.e., pure-bloods).
PS: Some additional proof from the upcoming movie may help get better info to improve the answer.
Grindelwald hates Muggles so he could be pureblood. But Tom Riddle was half blood and he hated Muggles and killed his father. So Grindewald could be half blood. I doubt he was a Muggle born because of how bad he went. He has an equal chance of being a pure blood as much as a half blood because Dumbledore was a half blood. But we will never know probably until late Fantastic Beasts movies.