When the rotating speed change of the pump exceeds 20% of the original speed, the calculated values of its performance parameters by the pump similarity law are greatly differentiated. In order to analyze and solve this problem, a surface function equation is constructed to predict the flow rate and axial power of the pump device based on the two parameters of the pump speed and the head of the pump device. The energy efficiency performance curve with nonlinear characteristics of the tubular pump device at different speeds is converted to a prediction model of the energy efficiency parameters of the tubular pump device at different speeds based on BP-ANN. Meanwhile, the input mode of the prediction model is determined to establish the network structure of BP-ANN. According to the verification by the experimental data, the absolute deviation of the predicted pump efficiency is less than 1 %, which meets the accuracy requirements of practical engineering applications. This model can provide a reference for variable speed regulation and performance conversion of pump devices.