A new adaptive technique is presented for the increase of the dynamic stiffness of the cutting tool in a lathe by active control of the tool vibration in the cutting speed direction. Due to the statistic properties of tool vibration that are induced by the stochastic behavior of chip formation process, the controller is based on the filtered-x LMS algorithm which controls an adaptive filter that is based on Wiener filter theory. Hence, the adaptation of the filtered-x LMS algorithm is gradient-based and it is based on a classical optimization technique, the method of steepest descent. In the cutting experiments a tool holder construction with integrated actuators, i.e. secondary sources was used. The cutting experiments shows that the adaptive technique presented in this paper enables an increase in the dynamic stiffness of the cutting tool, i.e. tool vibrations are suppressed.