Screw rotors are mainly used in compressors, screw pumps and other equipment, and their surface quality plays a key role in service performance and service life. Process parameters are one of the main factors affecting the surface roughness of screw rotors. In order to explore the influence of process parameters on the surface quality of helical surface milling, a rotor milling experiment was designed to obtain prediction and experimental comparison samples. The improved northern goshawk search algorithm (INGO) is used to optimize the initial weights and thresholds of the BP neural network, so as to improve the prediction accuracy of the surface roughness of the milled multi-head screw rotor. Experimental results verify the prediction accuracy of the proposed algorithm. The results show that the proposed prediction model outperforms GRU neural network and CNN-GRU neural network models in terms of average training accuracy and prediction accuracy. The average training accuracy and prediction accuracy are about 94. 502% and 95. 523% respectively. Therefore, the proposed algorithm has high prediction accuracy and can provide a theoretical basis for reasonable selection of processing parameters of screw rotor milling.