In manufacturing industries of metallic molds, various NC machine tools are used. We have already proposed a desktop NC machine tool with compliance control capability to automatically cope with the finishing process of LED lens molds. The NC machine tool has an ability to control the polishing force acting between an abrasive tool and a workpiece. The force control method is called impedance model force control. The most effective gain is the desired damping of the impedance model. Ideally, the desired damping is calculated from the critical damping condition in consideration of the effective stiffness in force control system. However, there exists a problem that the effective stiffness of the NC machine tool has undesirable nonlinearity. The nonlinearity gives bad influences to the force control stability. In this paper, a fine tuning method of the desired damping is considered by using neural networks. The neural networks acquire the nonlinearity of effective stiffness. The promise is evaluated through an experiment.