The modulated model predictive control (MMPC) technique has shown promise in high-performance motor control. However, the vector duty cycle calculation of the MMPC method is still dependent on the cost function (CF), which has a certain error. To address this issue, a CF-free MMPC method based on geometric derivation is proposed. This technique utilizes the relationship between vector projection and geometry to accurately calculate the duty cycle, ensuring excellent steady-state performance. In addition, the duty cycle calculation inaccuracy of the MMPC method using three existing CFs is vividly evaluated by a 3-D visual analysis method in this article. Finally, the hardware-in-the-loop (HIL) and the experiment tests on a permanent magnet synchronous motor (PMSM) have been carried out. The results have verified the feasibility and effectiveness of the proposed CF-free MMPC technique.