This study proposes a new topology optimization framework that can design the transmitter (Tx) ferrite and receiver (Rx) coil to maximize the transfer power while satisfying the given constraints (the ferrite mass and IC-NIRP magnetic field regulation in this study). To evaluate the electromagnetic performance, a 3-D finite element analysis is performed at every optimization iteration. In the Tx design domain, the design variables are the relative "ferrite" densities of the finite elements, which can represent ferrite or air. Similarly, in the Rx design domain, the design variables are the relative "copper" densities of the finite elements, which can represent copper or air. As a result, the optimized Tx ferrite and Rx coil can satisfy the required charging voltage (5V in this study) with a minimal Rx coil weight. The effectiveness of the proposed work was compared to the result of the original coil layout optimization. The optimized results were manufactured and experimentally validated.