This paper investigates the shock isolation characteristics of an electromagnetic bistable vibration isolator (BVI) with tunable magnetic controlled stiffness. The theoretical model of the BVI is established. The maximum acceleration ratio (MAR), maximum absolute displacement ratio (MADR), and maximum relative displacement ratio (MRDR) are introduced to evaluate the shock isolation performance of the BVI. The kinetic and potential energy are observed to further explore the performance of the BVI. The effects of the potential barrier, shape of potential well, and damping ratio on the BVI are discussed compared with the linear vibration isolators (LVIs). The results demonstrate that the intrawell oscillations and snap-through oscillations are determined by the excitation amplitude and duration time of main pulse. MADR and MRDR of the BVI are smaller than those of the LVI. The maximum acceleration peak amplitude of the BVI is far below that of the LVI, especially when the snap-through oscillation occurs. In brief, the proposed BVI has a better shock isolation performance than the LVI and has the potential to suppress the shock of space structures during the launch and on-orbit deploying process.