Cost prediction for construction projects provides important information for project feasibility studies and design scheme selection. To improve the accuracy of early-stage cost estimation for construction projects, an improved neural network prediction model was proposed based on BP (back propagation) neural network and Snake Optimizer algorithm (SO). SO algorithm is adopted to optimize the initial weights and thresholds of the BP neural network. Cost data for 50 construction projects undertaken by Shandong Tianqi Real Estate Group in China was collected, and the data samples were clustered into three categories using cluster analysis. 18 engineering feature indicators were determined through a literature review and 10 feature indicators were selected using Boruta algorithm for the input set. Compared to BP neural network and PSO–BP neural network, the results show that the improved SO–BP model has higher prediction accuracy, stability, better generalization ability and applicability. Therefore, based on reasonable feature indicators, the method proposed in this paper has certain guiding significance for predicting engineering costs.