Government-invested construction project (GICP) has a great significance to social and economic development but suffered many risks due to its large scale, huge investment, and long construction period. The risks in GICP are complex so as to lead the project to failure; it is extremely urgent to take the risk management of GICP. This study establishes a risk early-warning framework to help the managers to understand the risk threat in advance, which supports them to make proper management strategies for the risk control. The whole framework can be concluded as three parts: information collection, data processing, and result prediction. Firstly, the 16 risk factors of GICP are identified. To express the hesitance of human decision and reduce the information loss in quantification, hesitant fuzzy linguistic term set (HFLTS) and triangular fuzzy number (TFN) are used to collect the experts’ linguistic term and transform them into numerical value. And then, these inputs are simplified into five factors based on principal component analysis (PCA), decreasing the impact of redundancy to risk early-warning. Meanwhile, the warning level is divided based on K-means, which avoids the subjectivity of experience decision. Further, the backpropagation neural network optimized by the genetic algorithm (GA-BP) is used to complete the simulation of risk value. The 75 groups of questionnaire data are used to train the network and the 10 groups are used as test set. The validation of the proposed framework has been verified with an average relative error in 7.2% and the average absolute error in 3.91. Finally, corresponding suggestions to prevent and control the different risks in GICP are put forward.