The African continent is projected to suffer adverse impacts from climate change, which are disproportionate to its contribution to global carbon dioxide emissions. Africa is particularly vulnerable because it is among the hottest places on the Earth and therefore any further warming will likely have adverse socioeconomic consequences; and most of the economies in this region rely mainly on natural resources and rain-fed agriculture, which are very sensitive to climate change and variability. This article investigates the impacts of climate change on African agriculture and discusses the policy implications for managing these impacts. The modelling results show that Africa will experience the largest impacts from climate change in terms of decline in economic growth and welfare losses. The disaggregated results show that Southern Africa will be the hardest hit region, followed by the Rest of sub-Saharan Africa, North Africa and East Africa, in that order. There is therefore need for concerted efforts at adaptation, which should include introduction of temperature-sensitive varieties, diversification of production systems and livelihoods, shift to sustainable agricultural intensification, shift to irrigation agriculture, addressing institutional challenges such as poor physical and social infrastructure, market imperfections, lack of access to credit, and lack of crop insurance, etc. In the long run, emphasis should be placed on diversifying away from agriculture to industry and services.