This paper proposes a coil design method for the magnetically coupled resonant wireless power transfer (MCR-WPT) system. Based on the Biot−Savart law, the magnetic flux density at the observation point was derived, and the magnetic flux of the observation plane generated by the exciting coil was deduced to build the calculation model of power transfer efficiency (PTE) and power delivered to the load (PDL). The PTE and PDL curves via coil parameters could be fitted in minutes using numerical calculation. The coil was designed according to transmission objectives and dimension constraints. In addition, the calculated PTE and PDL were compared with those from finite element analysis to verify the credibility of the method. Finally, the actual curves of PTE and PDL were achieved, which showed a strong positive correlation with the corresponding curves from the calculation model. The relative average deviations of PDL curves were less than 6.11%. Meanwhile, coils designed with the numerical calculation could realize 309.80 W and 88.51%, which achieved the objectives under the constraints. The results demonstrate that the proposed method can realize a rapid and accurate coil design under constraints. It can also be applied to other coil structures or circuit topologies with strong universality.