A control device for a machine tool provided in the machine tool comprising a cutting tool for cutting a workpiece (W), rotating means for rotating the workpiece (W), feeding means for feeding the cutting tool and the workpiece (W) in a predetermined feed direction, and vibration means for reciprocally vibrating the cutting tool and the workpiece (W) relative to each other, wherein the control device comprises; a control section for making the machine tool perform vibration cutting to the workpiece (W) via the rotation of the workpiece (W) and via feeding of a cutting tool to the workpiece (W) with reciprocal vibrations, user inputting means for inputting a number of rotations (S) or a number of relative vibrations (N) of the cutting tool and the workpiece (W), presenting means for extracting a plurality of combination candidates of each parameter consisting of a number of rotations (S) and a number of vibrations (N) from a combination table showing the relationship of the numbers of rotations (S) or the numbers of vibrations (N) with each vibration frequency (f) of a vibration frequency group (f) that is a group of vibration frequencies (f) dependent on a period, in which an operating instruction can be executed to the vibration means , and any number of vibrations (N) or number of rotations (S), in order of approximation to the input value of the number of rotations (S) or the number of vibrations (N) that is input via the user inputting means , and selectably presenting a plurality of the extracted combination candidates of each parameter to the user, and setting means for setting each parameter of the number of rotations (S) and the number of vibrations (N) in the control section on the basis of a predetermined combination selected from a plurality of the combination candidates of each parameter that are got selectable by the presenting means . wherein the control device comprises; a control section for making the machine tool perform vibration cutting to the workpiece (W) via the rotation of the workpiece (W) and via feeding of a cutting tool to the workpiece (W) with reciprocal vibrations, user inputting means for inputting a number of rotations (S) or a number of relative vibrations (N) of the cutting tool and the workpiece (W), presenting means for extracting a plurality of combination candidates of each parameter consisting of a number of rotations (S) and a number of vibrations (N) from a combination table showing the relationship of the numbers of rotations (S) or the numbers of vibrations (N) with each vibration frequency (f) of a vibration frequency group (f) that is a group of vibration frequencies (f) dependent on a period, in which an operating instruction can be executed to the vibration means , and any number of vibrations (N) or number of rotations (S), in order of approximation to the input value of the number of rotations (S) or the number of vibrations (N) that is input via the user inputting means , and selectably presenting a plurality of the extracted combination candidates of each parameter to the user, and setting means for setting each parameter of the number of rotations (S) and the number of vibrations (N) in the control section on the basis of a predetermined combination selected from a plurality of the combination candidates of each parameter that are got selectable by the presenting means . <EOS>