The transfer coils of traditional Magnetic Coupling Resonant Wireless Power Transfer (MCR-WPT) systems are generally arranged coaxially. Coplanar coils can be an alternative scheme that can save more space in some applications, such as mobile phone wireless charging. However, the inductances of coplanar coils are sensitive to foreign objects, which leads to a reduction in transfer efficiency and output power. A MCR-WPT system with coplanar coils and its control strategy are proposed in this paper. First, the characteristic of the mutual inductance and the magnetic field distribution between the coplanar coils are analyzed. A formula to calculate mutual inductance between the coplanar coils is proposed in this part. Secondly, the effect of inductance offset and frequency detuning on transfer efficiency and output power are analyzed. Then, the control strategy to eliminate frequency detuning is proposed. The proposed method implements switched capacitor to take place of constant compensation capacitor. The equivalent capacitance of switched capacitor is adjusted when the frequency detuning occurred. Thus, the inherent frequency of the resonant tank tracks the source frequency all the time. Since the switched capacitor of each side is controlled based on the quantity of their own, the control process is independent and does not require wireless communication. The complexity and the cost of the system are reduced. At the end of the article, the veracity of mutual inductance formula and the effectiveness of the proposed control strategy are verified by experiments. The experimental coils are placed in in an environment full of interference. The inductances of the coils are reduced from 224 µH to about 214 µH. The transfer efficiency and output power of MCR-WPT system with closed-loop control are higher than the one without control. At a distance of 5 cm from edge to edge, the transfer efficiency is 76.37% under the proposed control and 72.21% under no control. The output power is 285.66 W under the proposed control and 271.37 W under no control.field distribution are different from the coaxial ones. There are some works that have analyzed the mutual inductance of coils with lateral misalignment [5] or with angular azimuth misalignment [6]. However, there is no research on the MCR-WPT system with coplanar coils. This kind of coils arrangement has been neglected before.Inductances of coils are very sensitive to external interferences. For instance, ferrite cores are used frequently in the design of coils to improve the mutual inductance. However, ferrite cores can change the distribution of the magnetic field [7]. Thus, the inductances of coils will vary significantly with misalignment. Metal objects outside coils can also cause the instability of inductances. Meanwhile, the capacitances of compensation capacitors in the MCR-WPT system may be affected by temperature, frequency, bias voltage, etc. Therefore, the inherent frequency of the resonant tanks consisting of an inductor and compensation capacitor is changed accor...