High ductility, high strength, high work hardening rate and low thermal conductivity of stainless steels are the main factors that make their machinability difficult. In this study, determination of the optimum cutting condition has been aimed at when fine turning an AISI 304 austenitic stainless steel using ceramic cutting tools. The cutting speeds for the turning test were from 80 to 320 m / min, feed rates were from 0.04 to 0.10 mm / rev and the depth of cut was fixed at 0.1 mm. According to the test results, we can find that the values of surface roughness were decreased when the cutting speed was increasing, and decrease with the decrease of feed rate. But when the cutting speed was greater than 360 m / min, or the feed rate was smaller than 0.02 mm / rev，the surface roughness would be deteriorated because of the chatter phenomenon. In this paper, a polynomial network is adopted to construct a prediction model on surface roughness for fine turning of AISI304 austenitic stainless steel. The polynomial network is composed of a number of functional nodes. These functional nodes are self-organized to form an optimal network architecture by using a predicted square error (PSE) criterion. It is shown that the polynomial network can correctly correlate the input variables (cutting speed and feed rate) with the output variable (surface roughness). Based on the surface roughness prediction model constructed, the surface roughness of the workpiece can be predicted with reasonable accuracy if the turning conditions are given and it is also consistent with the experimental results very well.