In wireless power transfers (WPTs), it is challenging to obtain a constant output of power (COP) and constant transmission efficiency (CTE) in large coupling variation ranges. In this study, the eight-coil WPT system achieves a uniform magnetic field (UMF) in the transmitter and receiver sides using two transmitting (Tx) coils and two receiving (Rx) coils, respectively. COP and CTE are then achieved with large coupling variation ranges. The circuit model and equations of the transmission characteristics are first obtained based on the structure and working principle of the Helmholtz coil. The model of the mutual inductance and equation of the impedance coupled factor are then developed. The laws of the transmission characteristic are also determined by adopting a simulation tool and equations of the transmission characteristics. Finally, the eight-coil WPT experimental system is designed. In a fixed-frequency mode, the COP and CTE are achieved when the coupling and misalignment distances are changed within a quarter or one-fifth of the relay coil diameter, respectively. This topology provides an efficient solution for problems faced in practical applications, such as wireless chargers of kitchen appliances and automatic mobile robots of small size.