The multiphase interleaved boost converter (MIBC) with coupled inductor has higher power density and efficiency. In order to improve the power density and efficiency of coupled inductor furtherly, an expandable coupled inductor is proposed and a universal design method is presented in this paper. In this design method, recursive operation is introduced to achieve accurate calculation of current ripple. The approximate model of magnetic reluctance is used to obtain the AC magnetic flux calculation method of the multiphase coupled inductor, which solves the problem of complexity and low accuracy of magnetic flux calculation. Finally, a three-phase coupled inductor is designed and the effectiveness of the method proposed in this paper is verified by simulation and experimental results.