BIM technology is an important technology for digitizing construction project management in order to improve management efficiency, and it has a supportive role in predicting the relevant indicators of project management. The article constructs a project management prediction model based on BIM technology that integrates GSVM and EVS. The earned value method is used to calculate the project schedule performance index and cost performance index, and the gray support vector machine is adopted to map the nonlinear data into the high-dimensional space and carry out calculations in order to simplify the complexity of calculations and improve the prediction efficiency and accuracy. The case study shows that the project duration was shortened by 21 days and 242,000 dollars reduced the cost by applying the model of this paper. Structural equations confirm the positive effect of BIM technology and the GSVM-EVM model on the performance of construction project management and the positive effect of BIM technology on the prediction effect of the GSVM-EVM model.