A machining simulation is performed on a graphic data basis prior to machining. Machining simulation means (17) simulates a forced-vibration frequency and/or a load variation frequency occurring due to interrupted cutting on the basis of machining information, and numerical control command generating means (18) generates a numerical control command on the basis of the frequencies obtained from the machining simulation means (17). A spindle rotation speed can be reflected on the actual machining and the generation of a machining program under conditions optimum for the actual machining. Therefore, the interrupted-cutting forced-vibration frequency and/or load variation frequency, or harmonic frequencies thereof which are integral multiples thereof are prevented from being close to the natural frequency of a machine, a tool, a jig or a workpiece. Thus, chattering due to resonance can be prevented, thereby improving a surface accuracy.