The technical focus of drilling operations is changing to oil and gas reservoirs with higher difficulty factors such as low permeability and fracture. During the drilling process, drilling operations in deep complex formations are prone to overflow and leakage complications. Leakage and overflow problems will change the performance of the drilling fluid in the wellbore, impacting the wellbore pressure, and causing complex accidents such as stuck drilling and collapse. In order to improve the level of control over the risk of wellbore overflow and leakage, it is necessary to predict the mud overflow and leakage situation and to arrange and control the risk of leakage and overflow that may occur in advance to ensure the safety of drilling. By using a genetic algorithm to optimize the multi-layer feedforward neural network, this paper establishes a GA-BP Neural Network Drilling overflow and leakage prediction model based on multi-parameter fusion. Through the optimization training of 14 parameters that may affect the occurrence of complex downhole accidents, the mud overflow and leakage are predicted. The prediction results of the model are compared with the prediction results of a conventional BP neural network, and verified by the real drilling data. The results show that the MAE, MSE, and RMSE of the GA-BP neural network model are improved by 2.91%, 4.48%, and 10.93%, respectively, compared with the BP neural network model, and the prediction quality is higher. Moreover, the amount of mud overflow and leakage predicted by using the GA-BP neural network matches well with the pattern of mud overflow and leakage data in real drilling, which proves the effectiveness and accuracy of the GA-BP neural network in overflow and leakage prediction.