Dry turning of Cr12MoV cold work die steel with cubic boron nitride (CBN) cutting tools is experimentally investigated using Taguchi orthogonal experiment method, in which the cutting speed, feed rate, depth of cut, and tool nose radius were considered as design variables. By making use of the nonlinear fitting ability of neural networks, coupled with the global searching ability of genetic algorithms, a model for predicting the machining surface roughness was established and an optimal combination of cutting parameters and tool nose radius giving the optimal surface roughness was found. The value of the optimal surface roughness obtained by genetic algorithms was reduced by 7.1% and 17.2%, respectively, as compared to the values of the optimal surface roughness obtained from the Taguchi method and turning experiments. The method used here provides theoretical reference for the modeling and parameter optimization of tool wear, cutting force and residual stress, and other problems in cutting process.