Semi-arid tropical rangelands substantially contribute to livelihoods of subsistence farmers, but are threatened by undesired vegetation shifts due to climate change and overgrazing. Grazing-induced shifts of the grass community composition are often associated with rangeland degradation. To identify sustainable management strategies, a process-based understanding of grass functional diversity and rangeland dynamics is required. We present a new scheme for aDGVM2, a dynamic vegetation model for tropical ecosystems, that distinguishes annual and perennial grasses based on trait trade-offs to improve the representation of rangeland communities. Additionally, the model includes a new scheme that describes selective grazing and grazing effects on grass-layer composition. We tested the new model version for various grazing intensities along a precipitation gradient in South Africa. Mean annual precipitation below 500 mm constrained rangeland productivity and carrying capacity. Increasing grazing intensity reduced rangeland productivity and increased annual grass abundance. Heavy grazing resulted in annual grass dominance. Livestock preferred perennial over annual grasses at low grazing intensities at all except the two driest sites; preference switched to annual grasses at intermediate intensities, and became non-discriminating at high grazing intensities. Rangeland recovery after removal of grazers required 2-15 years. We conclude that management intervention reducing or eliminating grazing pressure during and after stress years is crucial to allow rangeland recovery and avoid permanent degradation.