The effects of Climate Change may have the potential to cause the weakening and breakdown of social and governmental structures. In this paper, we construct a fragile index evaluation model to determine the fragility of different countries and measure the impacts of Climate Change. In the first part, by selecting 10 indicators on economic, political, social and national cohesion, we establish a fragile index evaluation model. Applying the calculation method of each indicator value and the Grey slope correlation model, we determine the weight of each indicator and obtain the fragile indicator value. Then we set up the five-level standards of fragility and determine the destructive levels of equally destructive climate disasters in different countries of fragility. In the second part, we study the fragility of Somalia. Based on the fragile index evaluation model, we obtain that Somalia is at a severe fragility level. Then, by analyzing the impact of the drought on the fragile index of Somalia, we obtain that the meteorological drought would cause ecological drought, hydrological arid and agricultural drought, moreover it would lead to food scarcity, environmental degradation and increased conflict, thus contributing to the increasing of the fragile index on Somalia. In the third part, we study the fragility of Cuba. According to the fragile index evaluation model, we conclude that Cuba is at a relatively stable level. By analyzing the historical data of the North Atlantic hurricane, we obtain that with the rising frequency of hurricanes and floods in the Caribbean would push up fragile index of Cuba. We also estimate that fragile degree of Cuba is likely to shift from a relatively stable level to a relatively fragile level within 30 years. In the fourth part, simulation with Global Mapper shows that the sea level rise of 1.5 meters would inundate most of Maldives territory, threatening the stability of the country seriously. While constructing the artificial island is a feasibility intervention to mitigate the threat. According to the economic situation of the country, we propose the phased construction plan with an estimated cost of 3-4 billion dollars. Finally, we test the sensitivity of model. The result shows this model is sensitive to the indicator values but insensitive to indicator weights. In order to adapt to the assessment of large area and small area, we propose the expansion of evaluation index and the optimization plan of weight distribution.