In the most general terms, you need to understand some things to get a good answer. Yes, simulation tools exist to create specific weather patterns, but they rely on general principles. Some things to consider:
You already know you want a massive grassland climate. So it must have the climate that grasslands have right here on earth (assuming earth-like biology, of course).
Grasslands form in nutrient-poor and low-rain areas. Periodic, naturally-occurring fires tend to promote grasslands. Therefore, this massive land area needs to be dry enough to prevent forests, wet enough to support grass, and have the right mix of nutrients in the soil.
There are examples of massive grasslands on earth: the Great Plains (mostly grass) and the Asian Steppe being two great examples. They get occasional rains and storms, but are mostly sunny most of the time.
Remember convection: hot liquids tend to rise, cool liquids get 'sucked in' below the now-vacant space where the hot liquid was. This happens on a massive scale in atmospheres. Instead of going from pole to equator, though, it forms zones/bands of moving air. These are called Hadley cells!
The question indicates that there is no equator. This can be due to several things: maybe the world is a ring-world (like in the Halo video game series) or the more likely Eyeball planet.
Eyeball planets are 'tidally locked' with their sun(s), so the same bits of land/ocean are always facing the sun. This results in climate oddities!
Combining this with Hadley cells means you could (in theory) have rings-of-climate with the "under the sun" point and "furthest from the sun" points acting like a hot/cold poles and the center point of the rings. Combine this with Hadley cells, and you get permanent winds which could (in theory) support a ring of grassland climates with the specified area.
Odd stuff would likely happen in Eyeball planets, though.
- The Hadley cells would result in a (permanent?) cold wind from the dark side to the day side.
- Water on the day side could be a source of rain/snow which feeds into the grasslands, although maybe not directly on the grasslands.
- Plants, including grasses, would always want the faces of their leaves/blades facing the sun, so every blade of grass would be arranged in the same direction.
- Travelling to/from the day/night side could be a part of daily life for animals.
Eyeball earths: they are really amazing!