Pumps consume nearly 8% of global electricity as the essential equipment for liquid transportation. A practical method for improving centrifugal pump energy efficiency is accurately predicting and controlling the pump operation status. However, current estimation methods for sensorless flow rate prediction have a significant error at low flow rate conditions. This study adds valve opening as the estimation model input variable, including motor shaft power and speed, to form a back-propagation neural network (BPNN) on an asynchronous motor-driven multistage centrifugal pump. By optimizing the initial weights and thresholds of BPNN, a GA-BPNN model was proposed to improve the prediction accuracy by using a genetic algorithm (GA). The results indicate that, with the addition of the valve opening as an input variable, the accuracy of BPNN-VO and GA-BPNN prediction improves significantly more than BPNN-NVO. Furthermore, the GA-BPNN model produces a significantly lower mean square error (MSE) and root mean square error (RMSE) than the original BPNN model. According to the experimental comparison and analysis, the absolute error of GA-BPNN between predicted flow rate and measured flow rate is less than 0.3 m3/h, the average relative error is less than 2%, and the relative error of low flow rate is less than 5%. This GA-BPNN estimation model significantly improves the accuracy of flow rate prediction, especially at small flow rates, and extends the scope of centrifugal pumps’ monitoring and control technology without flow sensors.