New energy private passenger vehicles play an important role in achieving the carbon peak target, and scientific and accurate prediction of sales volume is the basic prerequisite for achieving the target. The traditional grey prediction model for new energy vehicles only considers the regularity of historical data and rarely considers the significant impact of new energy vehicle sales data on future trends, resulting in differences between the model's prediction results and qualitative conclusions. To improve the accuracy of the model and reduce errors, this article uses the real number field fractional order grey generation operator to optimize the three-parameter discrete grey prediction model. Based on the principle of new information priority and combined with rolling mechanism, a three-parameter discrete grey rolling model is constructed to predict the sales of new energy private passenger vehicles in China. The results show that the sales of new energy private passenger vehicles in 2030 are 6.849~5 million units, which can achieve 88.15 of the carbon peak target for the current year. Based on the predicted values, countermeasures and suggestions are proposed to promote sales.