© 2021, The Author(s), under exclusive licence to Springer Nature B.V.This work proposes a novel two-dimensional (2D) graded core with anti-tetrachiral cells and evaluates the numerical vibroacoustic response of sandwich panels with these particular cores. First, a homogenization scheme is utilized to model the sandwich structure, followed by a modal analysis of the homogenized model in the frequency range of 0–200 Hz. The results have been compared with those obtained from an exact and full-scale finite element model of the sandwich structure. A general good agreement has been observed for the first six natural frequencies. Next, the radiated sound power level in the frequency band of 0–200 Hz is calculated and minimized for different geometry parameters of the sandwich structure. A hybrid design optimization approach using method of moving asymptotes and genetic algorithm is used. The optimized 2D gradient configurations show a significant 78% reduction of the normalized radiated sound power level and a 15% increase of the fundamental frequency, compared to the baseline sandwich panel configurations.