In construction project management, accurate cost forecasting is critical for ensuring informed decision making. In this article, a construction cost prediction method based on an improved bidirectional long- and short-term memory (BiLSTM) network is proposed to address the high interactivity among construction cost data and difficulty in feature extraction. Firstly, the correlation between cost-influencing factors and the unilateral cost is calculated via grey correlation analysis to select the characteristic index. Secondly, a BiLSTM network is used to capture the temporal interactions in the cost data at a deep level, and the hybrid attention mechanism is incorporated to enhance the model’s feature extraction capability to comprehensively capture the interactions among the features in the cost data. Finally, a hyperparameter optimisation method based on the improved particle swarm optimisation algorithm is proposed using the prediction accuracy as the fitness function of the algorithm. The MAE, RMSE, MPE, MAPE, and coefficient of determination of the simulated prediction results of the proposed method on the dataset are 7.487, 8.936, 0.236, 0.393, and 0.996%, respectively, where MPE is a positive coefficient. This avoids the serious consequences of underestimating the cost. Compared with the unimproved BiLSTM, the MAE, RMSE, and MAPE are reduced by 15.271, 18.193, and 0.784%, respectively, which reflects the superiority and effectiveness of the method and can provide technical support for project cost estimation in the construction field.