Ni-based alloy Inconel 625 has extensive applications in aerospace, aircraft, marine, chemical, and oil and petrochemical industries. However, machining Inconel 625 is challenging due to its superior mechanical properties, along with its tendency to work harden quickly. In this context, this study consisted of turning operation of Inconel 625, carried out by coated carbide inserts. The response parameters were evaluated in terms of cutting speed, feed rate, and depth of cut. The L27 orthogonal array was thus selected for the study. The machined surfaces of samples were inspected for surface roughness parameters using Taylor Hobson Talysurf 4 instrument. The feed-forward back propagation was selected and used as the algorithm. For surface roughness ANN predictive model, three input parameters were taken as three nodes in the input layer and four surface parameters as four nodes in the output layer. 3-20-4 neural network structure for Inconel 625 material helped in the best way to compare actual values and the ANN predictive model for surface roughness in turning operation. Also, ANN predictive model was developed for MRR, considering 3-7-1 neural network structure. The MAPE in the prediction of response performance by the predictive model were 6.534 and 5.550, respectively, for training and testing the surface roughness model. For MRR model, MAPE in the prediction were 2.3851 and 3.9731, respectively, for training and testing. It was concluded that the ANN gave very good performance for the surface roughness parameters and the MRR.