The wireless power transfer technology has been applied to the robot charging system based on its safety and reliability. In order to improve the coupling performance of the system and reduce the electromagnetic radiation around the coil, a magnetic coupling resonance of a novel semi-enclosed magnetic core structure is proposed. Firstly, the magnetic circuit model is established with a disc core, and the expressions about coupling coefficient are derived, which provide the basis for designing magnetic core structures. The reluctance of mutual-coupling area is reduced by adding a certain height magnetic ring on the outer edge of the transformer with disc core. Meanwhile, a certain inner diameter of the core is removed from the bottom core to increase the reluctance of self-coupling area. Secondly, the magnetic circuit model of the new Semi-enclosed magnetic core is established, and the coupling coefficient expression of the new magnetic core system is derived. Three structural parameters (magnetic ring wall thickness, magnetic ring height, core inner diameter) affecting the system performance are obtained. Based on Ansys Maxwell simulation, three parameters impact is analyzed for the coupling coefficient and electromagnetic radiation, and the magnetic core structure parameters are optimized by parameter scanning. Finally, the simulation results are verified by setting up an experimental platform. Compared with the system with a disc core, the new Semi-enclosed core structure has a 5.1% improvement in the coupling coefficient, and the new core offers 1.46 times improvement in the shielding effect under the coil.