Livestock production is important for local food security and as a source of income in sub-Saharan Africa. The human population of the region is expected to double by 2050, and at the same time climate change is predicted to negatively affect grazing resources vital to livestock. Therefore, it is essential to model the potential grazing output of sub-Saharan Africa in both present and future climatic conditions. Standard tools to simulate plant productivity are dynamic vegetation models (DVMs). However, as they typically allocate carbon to plant growth at an annual time step, they have a limited capability to simulate grazing. Here, we present a novel implementation of daily carbon allocation for grasses into the DVM Lund-Potsdam-Jena General Ecosystem Simulator (LPJGUESS) and apply this to study the grazing potential for the Kordofan region in Sudan. The results show a latitudinal split in grazing resources, where the northern parts of Kordofan are unexploited and southern parts are overused. Overall, we found that the modeled grazing potential of Kordofan is 16% higher than the livestock usage reported in the Food and Agricultural Organization of the United Nations, indicating a mitigation potential in the form of a spatial relocation of the herds.