This paper proposes the design method using a numerical formula known as the Advanced Inverse Cosine Function (AICF) to reduce vibration of the Interior Permanent Magnet Synchronous Motor (IPMSM). The proposed method reduces the vibration by modifying the rotor shape based on the numerical formula that makes the air-gap flux density sinusoidal under certain load condition. The radial electromagnetic force that is the source causing the vibration of the motor is related to the air-gap flux density under load condition. Therefore, the AICF which reduces the magnitude of the harmonic of the air-gap flux density is derived in this paper and the radial electromagnetic force due to the harmonic of the air-gap flux density decreases applying the AICF. To verify the validity of the proposed method, an 8 pole 12 slot prototype applied with the AICF is proposed. Using the Finite Element Analysis (FEA), the radial electromagnetic force and the displacement of the prototype with the AICF are compared with those of the normal model without the AICF. Finally, the results of the vibration test of the normal and AICF models are compared.