The acoustic black hole (ABH) is a feature commonly found in thin-walled structures that is characterized by a diminishing thickness and damping layer with an efficient wave energy dissipation effect, which has been extensively studied. The additive manufacture of polymer ABH structures has shown promise as a low-cost method to manufacture ABHs with complex geometries, exhibiting even more effective dissipation. However, the commonly used elastic model with viscous damping for both the damping layer and polymer ignores the viscoelastic changes that occur due to variations in frequency. To address this, we used Prony exponential series expansion to describe the viscoelastic behavior of the material, where the modulus is represented by a summation of decaying exponential functions. The parameters of the Prony model were obtained through experimental dynamic mechanical analysis and applied to finite element models to simulate wave attenuation characteristics in polymer ABH structures. The numerical results were validated by experiments, where the out-of-plane displacement response under a tone burst excitation was measured by a scanning laser doppler vibrometer system. The experimental results illustrated good consistency with the simulations, demonstrating the effectiveness of the Prony series model in predicting wave attenuation in polymer ABH structures. Finally, the effect of loading frequency on wave attenuation was studied. The findings of this study have implications for the design of ABH structures with improved wave attenuation characteristics.