Magnetic resonance wireless power transmission consists of a source coil and relay coil (transmission coil (Tx-coil), receiving coil (Rx-coil)). The relay coil is designed with windings and a series capacitor, which are resonant with the input voltage frequency. Magnetic resonant wireless power transmission by a relay coil enables the transmission of power from a few centimeters to several meters. Recently, research has been conducted on the shape and material of each coil to increase the transmission distance. However, limitations remain with respect to increasing the transmission distance. Specifically, the optimization of the electrical characteristics of the relay coil is necessary to increase the transmission distance and improve efficiency. In this study, we configured the inductance of the relay coil to be approximately 95 μH, 270 μH, and 630 μH. Accordingly, we designed the series capacitors to have the same resonant frequency and analyzed the transmission characteristics of each relay coil. We confirmed that as the inductance increased, the transmission efficiency increased by up to 10%. The relay coil was designed to have an inductance of approximately three to six times that of the source coil (load coil). Thus, the optimal design of the relay coil is believed to be the most efficient and economical coil design.