Magnetic negative stiffness structure has the problem of nonlinearity in engineering applications, which is not conducive to the system’s stable operation. To address this problem, a new negative stiffness structure model, a nine-magnet structure, is proposed based on three-magnet and five-magnet structures. Based on the equivalent load method, an analytical model of the magnetic force and stiffness of the new negative stiffness structure is established. The negative stiffness curves of the three-magnet, five-magnet, and the new negative stiffness structure under the same parameter conditions are analysed. The nonlinearities of the three types of structures are compared and analysed. Finally, the vibration isolation performance of the new negative stiffness structure is dynamically analysed from the absolute displacement transfer rate perspective. The results show that compared with the three-magnet and five-magnet structures, the new negative stiffness structure has a weak nonlinear characteristic while taking into account the action value, and the nonlinearity is optimized, while the vibration isolation performance of the linear vibration isolation system connected in parallel with the structure is also improved.