In the design process of vibration isolators, the natural frequency is reduced by decreasing the structural stiffness. However, they still face the problem that the transmissibility is relatively high when the vibration isolator resonates. Acoustic Black Hole (ABH) structures, leveraging their damping enhancement effect and dynamic vibration absorption effect, have been widely applied in the field of vibration reduction. In this study, a new type of vibration isolator structure with integrated high load-bearing, vibration absorption, and isolation functions was designed by combining the sinusoidal beam structure and the acoustic black hole structure. This structure consists of a sinusoidal beam bearing frame and an internal ABH, and achieves vibration isolation through the combined action of the vibration isolation effect of the frame and the vibration absorption effect of the internal ABH. The finite element method and experiments were used to investigate the static performance of the structure, its dynamic performance under different loads, the influence of filling rubber on the structural performance, and the changes in its dynamic performance before and after the installation of the ABH. The results show that filling the sinusoidal beam structure with rubber creates a vibration isolation structure with high load-bearing capacity, high damping, and relatively low stiffness. This vibration isolation structure has a low modal frequency under its load-bearing limit, which can achieve the goal of low-frequency vibration isolation. In addition, attaching a ABH to the structure can effectively reduce the peak value of the resonance peak of the vibration isolator by utilizing the dynamic vibration absorption principle and damping enhancement.