In wireless power transfer (WPT) systems, it is well known that the series-parallel (SP)-compensated topology is preferable for large load systems, like biomedical implants and consumer electronics, etc. However, it is a major challenge for practical SP-compensated WPT applications to obtain efficient and stable power transfer characteristics under the variations of coupling coefficient and resonant frequency. Therefore, based on fractional-order (FO) circuit theory, this paper proposes an SP-compensated FOWPT system with coupling independence and detuning insensitivity. Experimental results show that stable output power is maintained with a constant transfer efficiency in a wide load range, and when the resonant frequency of the receiver is detuned ±5%, the fluctuations of output power and transfer efficiency are less than 1%. The experiment validates the effectiveness of the proposed system.