The Grade-H high strength steel is used in the manufacturing of many civilian and military products. The procedures of manufacturing these parts have several turning operations. The key factors for the manufacturing of these parts are the accuracy, surface roughness (Ra), and material removal rate (MRR). The production line of these parts contains many CNC turning machines to get good accuracy and repeatability. The manufacturing engineer should fulfill the required surface roughness value according to the design drawing from first trail (otherwise these parts will be rejected) as well as keeping his eye on maximum metal removal rate. The rejection of these parts at any processing stage will represent huge problems to any factory because the processing and raw material of these parts are very expensive. In this paper the artificial neural network was used for predicting the surface roughness for different cutting parameters in CNC turning operations. These parameters were investigated to get the minimum surface roughness. In addition, a mathematical model for surface roughness was obtained from the experimental data using a regression analysis method. The experimental data are then compared with both the regression analysis results and ANFIS (Adaptive Network-based Fuzzy Inference System) estimations.