<p>The three-coil structure is one of the effective solutions to extend the transfer distance of the MCR-WPT (magnetically-coupled resonant wireless power transfer) system. Therefore, it is very important to study the influence of the relay coil spatial position on the transfer performance of the WPT system. The circuit model is simplified based on the coupling structure. The voltage and current equations are established, and the expression of the output power and transfer efficiency are derived. Through analyzing the relationship between different types of coil offsets and mutual inductance, the law between relay coil offset and system output characteristics was obtained. The law is verified based on the extreme value theory: When the load and the internal resistance of the power supply are equal, the system output power is maximized when the axial offset position of the relay coil is equidistant from the transmitting and receiving coils. When the power supply internal resistance is large, the position of maximum output power is closer to the transmitting coil. When the load is large, the position of maximum output power is closer to the receiving coil. The optimal axial offset position for transfer efficiency is always near the transmitting coil, but this position shifts toward the receiving coil as the load increases. Increases in radial and angular offsets reduce both output power and transfer efficiency, but the change is gradual within a certain range of offset. Therefore, the output performance of the system can be improved by changing the position of the relay coil. Finally, the correctness of the theory and simulation is verified by experiments.</p>