According to the tool path characters of non-cylindrical hole precision machining by giant magnetostrictive components, a dynamic hysteresis model of giant magnetostrictive components was established by a pure delay transfer function and the linearity model between high-frequency driving currents and micro-displacement responses. The pure delay compensation parameters of the system were obtained by the relevant identification of driven currents and output displacements with a certain frequency. Then, a mapping model of the driven currents and output displacements without delay was established. The output displacement met the ideal tool paths of non-cylindrical hole boring by direct inverse model and delay compensation in real-time control. The results in verification experiments indicate that the maximum control error is 2.7 μm, and the maximum relative error is about 10%. By integration of micro-displacement feedback control,the accuracy of the component is improved further, the maximum control error is 1.2 μm, and the maximum relative error is about 7%.