This paper is about predicting the surface roughness by means of neural network approach method on machining of an engineering plastic material. The work material was an extruded PA6G cast polyamide for the machining tests. The network has 2 inputs called spindle speed and feed rate for this study. Output of the network is surface roughness (Ra). Gradient Descent Method was applied to optimize the weight parameters of neuron connections. The minimum Ra is obtained for 400 rpm and 251 cm/min as 0.8371 mu m.