Addressing the issues of low prediction accuracy and slow computation speed in existing cost prediction methods for the Engineering-Procurement-Construction (EPC) turnkey contracting model, this study proposes an improved generalized regression neural network prediction model based on a multi-universe optimization algorithm. The model employs an adaptive mechanism to regulate the exploration and exploitation phases of the algorithm, uses the optimization algorithm to determine the optimal smoothing factor, constructs the cost prediction model, and applies the entropy weight method to determine the weighting ratios of the indicators. Experiments show that the model converges faster, achieving maximum convergence accuracy of 10100 after 50 iterations. The minimum root mean square error is 0.04 and 0.06 lower than other algorithms, and the F1 values are 13.2% and 11.4% higher than the two algorithms, respectively. A prediction error of the main structure of the model is 3.9%, which is 4.6% and 1.7% lower than other algorithms, and the prediction error of the foundation engineering is +2.8%. The total cost predicted by the model exceeds the actual construction cost by 4.8688 million yuan, with a prediction error of 3.07%. This is less than the allowable deviation of ±5% for construction cost predictions. Therefore, the total cost proposed by the study exceeds the cost prediction model, which can effectively improve the accuracy of cost predictions while significantly increasing the speed of model calculations, thereby optimizing decision-making and cost management efficiency for engineering projects.