This article introduces a novel method to enhance the damping performance of triply periodic minimal surface (TPMS) structures by integrating metamaterials with constrained layer damping (CLD) applications. This objective is accomplished by combining a viscoelastic silicone polymer layer with a primitive TPMS structure fabricated through laser powder bed fusion using aluminum alloy powder. Finite‐element method (FEM) models using voxel elements, due to their high accuracy and computational efficiency, are developed to analyze the damping behavior of the TPMS‐based CLD structure across various frequencies. Experimental modal test results validate the FEM model with high accuracy. Two distinct damping characterization methods, both time‐domain and frequency‐based, are employed to quantify the damping performance. The results reveal a fivefold improvement in damping performance in the time domain compared to the metal TPMS structure. In the frequency domain, the structure demonstrates 76% lower cumulative vibration compared to the metallic reference using the integral of frequency response method.