Xinjiang is facing a new historical opportunity and challenge about the economic development, under the new situation which building "the Silk Road Economic Belt" together. Writer taking Xinjiang 2000-2012 years of economic growth and carbon emissions' data, and using the method of data analysis and Grey relation analysis to study the relationship between Economic Growth and Carbon emissions in Xinjiang. The conclusion shows the relationship between economic growth and Carbon emissions did not reflect on the inverted "U" curve relationship as the environmental Kuznets curve hypothesis described. There existed significant correlation degree between economic growth and carbon emissions in Xinjiang. The faster economy growth increases, the more carbon emission add. In a word, the quality of the economy is not optimistic. Then, through the quantitative research, the paper gives countermeasures and provides a theoretical basis to achieve the Xinjiang carbon emission reduction and the "new target of the construction of the Silk Road Economic Belt in the core area".