In a context marked by the increase in extreme climatic shocks, and the decline in the political stability of States in Sub-Saharan Africa (SSA), this article aims to analyze the effect of climate change on the political stability of 45 countries of sub-Saharan Africa over the period 2000-2020. Thus, we use time-country fixed effects to mitigate possible endogeneity biases. Our results obtained by Two-Way Fixed effets (TWFE) estimator indicate that climate change reduces political stability in SSA. Indeed, rising temperatures and falling precipitation reduce the political stability of these countries and vice versa. Furthermore, through the marginal effects, we show that wheat price volatility reduces the significant and positive effect of heavy rainfall on political stability, while rising wheat prices aggravate the negative effect of rising temperatures on political stability. The Generalised Method of Moments in System (GMM-S) and the method of lagged explanatory variables allowed us to better take into account the endogeneity problem, and to validate the robustness of our results. To reduce the risk of political instability in SSA, we recommend the development of effective methods of adaptation or mitigation of the effects of climate change, through the preservation of the environment, the promotion of green energies and the strengthening of infrastructure water management and storage, for agricultural populations. Furthermore, stabilizing food prices requires increasing the level of national and regional stocks of various foodstuffs.