As a low-carbon and cost-effective clean energy source, natural gas plays an important role in achieving China's “Dual Carbon” target. In this article, a new three-parameter discrete grey prediction model is used to simulate and forecast the production and consumption of natural gas in China from the perspective of background value optimization. Then the minimum mean absolute percentage error as the objective function from the perspective of fractional order cumulative generation in the real number field. Last, a fractional order in the real number field three parameter discrete grey prediction model TDGM(1,1,z,r(R)) is constructed under the condition of optimal background value. Then we use the model to simulate and predict China's Natural Gas External Dependence (NGED) under the “Dual Carbon” target. The results show that the performance of the new model is better than that of the traditional model GM(1,1) and DGM(1,1), thus proving the practicability and effectiveness of the new model. Put forward relevant policy suggestions according to the prediction results of China's NGED, and provide decision-making reference for the Chinese government to achieve the “Dual Carbon” goals.