During the COVID-19 epidemic, the Chinese central government adopted a dynamic clearing prevention and control strategy. Meanwhile, most local governments issued policies to incorporate normal epidemic prevention costs into the costs of construction projects. However, there are few provisions on how to determine the calculation standards for these costs. To accurately predict the normalized epidemic prevention costs of construction projects from different aspects, the relevant factors that affect epidemic prevention costs are investigated and an optimized neural network prediction method that can effectively eliminate abnormal data with a too large deviation is proposed. The results show that compared with the traditional backpropagation (BP) neural network and BP neural networks optimized by genetic algorithm, the error of the optimized neural network achieves a smaller error in predicting the normalized epidemic prevention costs of construction projects (the average error of the traditional BP neural networks is 6%). Meanwhile, among the factors that affect epidemic prevention costs, total investment, project category, and construction scale have the greatest impact. Based on the research results, this paper proposes pricing suggestions and corresponding management solutions for the epidemic prevention costs of construction projects, which will be helpful to project managers.