A control device for a machine tool comprising a control section for independently controlling each of relative movements between two cutting tools (130, 230) and a workpiece, the control section being capable of controlling the relative movements to cut the workpiece with a first cutting tool and a second cutting tool each vibrating, wherein the control section is configured to set a phase of a vibration waveform of each of the first cutting tool and the second cutting tool such that routes of cutting edges of the first cutting tool and the second cutting tool intersect routes of the cutting edges in a previous machining of each other of the first and second cutting tools (130, 230), and to perform cutting of the workpiece with an air-cut caused by the intersection of the route of the cutting edge of the first cutting tool and the route of the cutting edge of the second cutting tool, which performed the previous machining, and with an air-cut caused by the intersection of the route of the cutting edge of the second cutting tool and the route of the cutting edge of the first cutting tool, which performed the previous machining, wherein the control section is configured to control independently the time when the vibrations of the first cutting tool and the second cutting tool start according to installation positions of the first cutting tool and the second cutting tool, and wherein the control section is configured to rotate the workpiece with respect to the cutting tools (130, 230) and the control section is configured to control, for each of the cutting tools (130, 230), a number of vibrations per rotation of the workpiece, an amplitude of the vibrations, and a phase of the vibrations on the basis of installation positions of the each of the cutting tools. the control section being capable of controlling the relative movements to cut the workpiece with a first cutting tool and a second cutting tool each vibrating, wherein the control section is configured to set a phase of a vibration waveform of each of the first cutting tool and the second cutting tool such that routes of cutting edges of the first cutting tool and the second cutting tool intersect routes of the cutting edges in a previous machining of each other of the first and second cutting tools (130, 230), and to perform cutting of the workpiece with an air-cut caused by the intersection of the route of the cutting edge of the first cutting tool and the route of the cutting edge of the second cutting tool, which performed the previous machining, and with an air-cut caused by the intersection of the route of the cutting edge of the second cutting tool and the route of the cutting edge of the first cutting tool, which performed the previous machining, wherein the control section is configured to control independently the time when the vibrations of the first cutting tool and the second cutting tool start according to installation positions of the first cutting tool and the second cutting tool, and wherein the control section is configured to rotate the workpiece with respect to the cutting tools (130, 230) and the control section is configured to control, for each of the cutting tools (130, 230), a number of vibrations per rotation of the workpiece, an amplitude of the vibrations, and a phase of the vibrations on the basis of installation positions of the each of the cutting tools.