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Calculating the shut-off head for centrifugal pumps poses significant challenges due to inaccuracies in existing empirical methods. This paper presents a predictive model based on extensive experimental data, employing a back propagation (BP) neural network optimized via grey theory and genetic algorithms (GAs). Data were collected from 141 single-stage volute centrifugal pumps, and grey theory was used to analyze nine critical parameters of the impeller and volute, yielding five optimal input schemes with correlation coefficients exceeding 0.6. The GA was utilized to optimize the weights and thresholds of the BP model. The training involved 121 samples, while 20 additional samples were used to evaluate the models against three established methods (throne, modified throne, and regression fitting). The results indicate that the optimal input scheme consists of four parameters (impeller diameter, blade wrap angle, inlet diameter, and rotational speed) with correlation coefficients greater than 0.7. Both the BP and GA-BP models achieved training regression coefficients approaching 0.999. Within the specific speed range of 22–215, the GA-BP model demonstrated superior performance to the BP model and the three established methods, with maximum testing errors of 10.0%, 20.6%, 20.7%, 19.9%, and 23.3%, and average relative errors of 3.9%, 5.0%, 8.4%, 8.1%, and 5.8%, respectively. This paper introduces a novel prediction model for the shut-off head with an accuracy of 96%, providing a valuable reference for hydraulic design and performance prediction in centrifugal pumps.