With the rapid development of the new energy vehicle (NEV) industry, it has become a critical component of modern productivity, offering immense potential for economic growth and environmental benefits. However, accurately predicting NEV trends, such as sales volume and the annual installed capacity of power batteries, remains challenging due to the high dimensionality of data and the limitations of existing predictive methods. In view of these challenges, this paper proposes a novel prediction method that combines Functional Principal Component Analysis (FPCA) and Generalized Regression Neural Network (GRNN) to forecast NEV sales and power battery installation trends. By employing FPCA to reduce the dimensionality of nine key variables and using GRNN to incorporate seven influencing factors, such as ownership and total energy consumption, the study constructs a robust predictive model. The GRNN model is further optimized using cross-validation, achieving a high level of accuracy. It is hoped that the proposed FPCA-GRNN method, which has demonstrated superior performance compared to traditional approaches such as BP neural networks and multiple linear regression, will serve as a valuable tool for predicting NEV development trends and provide guidance for industry growth and policy-making in the NEV sector.