As a measure of the sustainability of a country, a state's fragility is attributed to numerous elements. Meanwhile, climate change is a potential global threat in the 21st century, which may further aggravate the fragility of countries. Concerning this issue, we propose an index system, the Fragile States Metric System (FSMS) to measure state fragility, which includes five dimensions: climate change, cohesion, economy, politics and society. Our FSMS consists of the Climate Change Metric System (CCMS) and Modified Conflict Assessment System (M-CAS). While establishing the model, we introduce a new hybrid evaluation method, Gray Relational Analysis (GRA)-Entropy method and variable weight function model, to calculate the weights. As the result, from 2007 to 2017, European countries, in particular Finland, Norway, Switzerland, Sweden and Denmark, remained the top 5 most stable countries. Robustness analysis proves that FSMS is a relatively stable model. In addition, in the application of FSMS, we introduce the economic theory, Pareto Optimum, to measure intervention costs while mitigating state fragility.