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• A novel 3D lattice structure combining the load bearing capability and broadband vibration suppression. • The acoustic black hole functional unit to realize the omnidirectional vibration bandgap in the low frequency domain. • Experimental validation of high stiffness-density ratio and ultra-wide vibration attenuation band. • Multi-optimization for superior static and dynamic properties. Multifunctional 3D lattice structures with unconventional mechanical properties offer unique material properties and broad applications in complex engineering environments. This paper proposes a novel 3D lightweight lattice structure based on the acoustic black hole (ABH) to achieve high load-bearing capability and vibration suppression in the low-frequency domain. In the microunit of the lattice structure, three ABH struts arranged in the X, Y, and Z directions are connected by a center stud and then assembled into a simple cubic lattice (SC) by a body-centered cubic (BCC) support. The proposed SC-BCC-ABH lattice structure is analyzed through simulation and experiments to investigate its static stiffness and vibration bandgaps. The results show that the Gibson-Ashby coefficient of SC-BCC-ABH is higher than that of typical lattice structures, indicating that superior stiffness is achieved. For vibration suppression, the proposed lattice structure generates a wide pseudo bandgap with a relative bandwidth of 0.81, which can be further increased to 1.17 by optimizing the structural parameters. The formation mechanism of the board bandgap is closely related to the ABH effect and the coupled vibration between ABH and SC parts. Parametric analysis and optimization procedures are carried out to obtain better static and dynamic performance. The SC-BCC-ABH lattice structure shows great application potential in micro-vibration isolation and impact protection for high-precision devices. [Display omitted] [ABSTRACT FROM AUTHOR]